Okay first of all, iguanas should not be living in a 5 gallon tank, second they shouldn't be living w/ any other animal, yet alone another iguana.
Iguanas and skinks need 2 different type of environments so either your iguana or your skink is not getting the environment they need.
Heat Rock REMOVE!!!! Heat rocks can seriously burn your iguana bad. Iguanas can not feel heat from there under bellys so they will lay on it and not realize that they are burning themselves. If you wish to use the heat rock, you can but ONLY IF the wiring is removed from the rock or not plugged in. You can go outside and find a rock that you've washed and cleaned and will get heat from the lights and will work just as good.
Have you taken your iguana to a herp/reptile vet who knows about iguanas yet? You should, he/she may have parasites or something else that you can not see, that the vet may. If you iguana has mites it could be killing your iguana and the mites could be transfered to your skink that it's living with.
Before you move your iguana into this larger tank from a friend, you will need to clean it out. If you use bleach, make sure that you rinse, rinse, rinse and re-rinse again. Do not leave a trace of bleach smell in it.
A young iguana should not be living in anything smaller then a 55 gallon tank. A 55 gallon tank will only hold them for 8-12 months of age, after that you will need to design an enclosure suitable for there size, it's always best to build bigger so you aren't rebuilding. Enclosure needs to be at least 1.5-2 times it's total length. An adult iguana will need an enclosure that is at least 6-7ft tall x 8-10ft long x 4ft wide.
While iguanas are living in tanks, you really shouldn't make it look "pretty", it should be just a housing for him/her to live in to keep it's temp, to have it's UVB, to have it's water, to have it's climbing space. If you try and make it look "pretty" you're taking away from the space that your iguana needs. Worry about how pretty you can make the full size iguanas housing look pretty over a tank, because they aren't going to be living in the tank for very long.
What you need for an iguana living in a tank is, no bad floor covering (meaning: bark, sand, dirt, pellets - anything like that that he/she could possibly lick up when they are tasting everything, when they lick they more then likely will swallow which then will cause blockage in there belly which you will sometime need to have surgically removed or it will cause the death of your iguana). Safe floor covering: newspaper (unprinted ink if possible), paper towels, vinyl floor covering, indoor/outdoor carpeting, towels. You need to wash the towels or indoor/outdoor before using, and if you have any lose fibers you will need to remove and replace. For the newspaper why I say unprinted, is because some newspapers in there ink it has soy. You can use newspaper and then place paper towels over the newspaper. If you iguana at some point tries to eat a lot of newspaper you will need to find a something else to use.
You may want to get more then just a stick. The stick is more then likely at an angle, which your iguana is not getting the proper UVB he/she needs. Iguanas need to lay flat under the UVB to properly get the UVB threwout the body, not just part of his/her body. When my iguana was in her tank, I used 3 branches from the pet store, and I layered in a way the sticks, and made sure it was sturdy. I had one branch (make sure it is wider then your iguanas body), flat under her UVB, the main bottom one was almost designed like a ladder, then I had another branch that I stuck between the ladder piece of wood and the flat one under the UVB to secure the one under the UVB more. You need to figure out a way to make the surface under the UVB as flat as you can not at an angle.
You can add fake silk leaves in the tank, make sure that you get leaves bigger then your iguana, they may try and eat the leaves, specially after you've sprayed them for humidity. You will also need to make sure that there is no exposed wiring from the fake leaves, if there is you will need to remove. You can place real plants in your iguanas enclosure but doing this you need to know which plants are safe and which plants are toxic. Also your iguana may try and eat them which will not allow him/her to eat the good staple greens he/she needs, why fake plants are recommended more.
You should have 2 dishes of water, one to drink from one to use the restroom in.
If you want it to look more tropical, at the pet stores you can buy those scenic backgrounds, you can place on the outside of the tank.
Your iguanas UVB: You should be using 2 UVB tubes not just 1. ReptiSun 10.0, Repti Glo 8.0 are the best for UVB, ReptiSun 5.0 is okay to use. There is a distance that your iguana needs to be from the UVB, and you will need to adjust as your iguana grows, the 5.0 and 8.0 is 6-8 inches away from your iguanas body, the 10.0 is 8-10 inches away from your iguanas body, again you need to adjust. This is why having a flat surface under the UVB is vital, w/out the proper UVB threw out your iguanas body he/she is not going to have that great of health, will not be able to process food, will not grow as good as he/she could. There are some UVB's that aren't the greatest to have.. the coil compact type do not produce the UVB your iguana needs, even though the packageing says it does, it doesn't, also another one that actually can cause eye damage to any and all reptiles is the "U" shaped, there has been a study on this.
Heat, a house bulb (wattage will depend on enclosure size) will produce enough heat for your iguana, you can use a basking bulb that you buy at the pet store, but the house bulb will work just the same but w/out the expense.
You can also get a CHE, a CHE is a (ceramic heat emitters), they produce no light just heat, so they are great to use at night (or day), and they are worth the money, they last for a few years.
Some iguanas dislike colored light, so at night if you are using a colored light and notice that your iguana is trying to hide from the light it could be causeing stress towards him/her. Plus they burn out w/in a few nights.
Temps are very vital for your iguana also, which w/ using a 5 gallon tank you are not providing. Never let drop below 70F ...
basking 92-96F if temp is too low digestion is slowed too high food digests too fast and nutrition is lost -
medium/middle 88-92F - cool 75-84F - at night 73-84F. The stick on glass type that you buy at pet stores are worthless they do not give the true temp. The best type of thermometer you can get is one w/ a probe at the end. You can place them more where your iguana is basking and can get a more true reading. Temp guns that you point at your iguanas body are truly the best because it will give a more true reading on what your igs body temp is.
This is just a small portion of an iguanas diet: daily food should have 5-7 good staple greens (2-3 cups a day if not more younger igs may not eat a 1/4-1/2 cup for a few months) ... collard greens, mustard greens, turnip greens, dandelion greens (if you can find), endive, radicchio, arugula, mache (if you can find), watercress ... some greens to give occasionally in small amounts kale, bok choy, escarole ... you can add some basil into the mix only w/ good staple greens, sometimes this helps the little ones eat ... some things to add (small amounts) snap peas, bell peppers (every now and then), parsnip, sweet potato/yam, acorn squash, butternut squash, buttercup squash ... fruits should only be given every now and then once or twice a week type of thing fruits are like junk food to iguanas ... some fruits to try papay, kiwi, mango, raspberries, strawberries, grapes, honeydew (great water source), canalope (great water source), 12 grain wheat bread (soaked) ... if anything has seeds make sure you remove seed before you give it to your iguana, for thinks like strawberries ones w/ small seeds, don't give for at least 3 days to pass threw system ... watermelon (seedless) can be frozen and then shaved onto your iguanas food helps w/ hydration everyday ... there are some foods that aren't good for your iguana: spinach has oxalate acids bind to the calcium, so even though spinach is high in calcium, almost none is actually available for the iguana to use, also the oxalate acids can form oxalate crystals which can and do build up in the kidneys causing kidney damage/failure ... some ig owners do give there ig spinach but in very small amounts and only once a month ... corn igs can not digest ... carrots aren't the greatest to give, can block calcium absorption and high in Oxalates, small amounts occassionally is fine ... food should be cut/chopped/diced no bigger then the iguanas head, if they are small having a chopper chop them up, or slice them into very small pieces ... spray/mist food to help w/ water/hydration ... there are some veggies/fruits that are toxic and can kill your iguana.
Here are some sites that I trust for iguana owners, please read:
http://www.greenigsociety.org/
http://www.iguanaden.org/
http://www.anapsid.org/iguana/index.html
If you'd like to read a book about iguanas, great book to read and have on hand:
Iguanas for Dummies by Melissa Kaplan
There are a few Yahoo groups for iguana owners, if you'd like to join, are very helpful to new iguana owners, again if you'd like to join:
http://pets.groups.yahoo.com/group/BabyIguana/
http://pets.groups.yahoo.com/group/IguanaDen/
Good luck w/ your new little one.