Thank you for the additional information. I know you've been trying to take good care of your turtles, but it appears that you received incorrect information when you bought them. That commonly happens because pet store personnel often don't really know how to take care of turtles. Unfortunately, the turtle owners don't know any better until their turtles get seriously ill, or even die. I'll try to help you as much as I can, but this turtle is very ill, and the chances of him surviving without the help of a veterinarian are slim.
First, I'm going to tell you about some changes you need to make to your set-up. These are essential and will help to keep your other turtles from getting sick. Otherwise, you're likely to lose all of them before this is over. If the 5 gallon tank is a hospital tank for the sick turtle, that's fine. However, if it's the permanent home for three turtles, you need to get a bigger tank as soon as possible. The minimum size needed for one baby turtle is 15 gallons. By the time they are a couple of years old, they need a 60 gallon tank. If the tank is too small, it doesn't matter what kind of filter you have or how often you change the water, the water quality will be poor. Water that looks sparkling clean still can have harmful amounts of ammonia and other chemicals in it. It doesn't take much to make a turtle sick. If you watch the classified ads, you can often buy used tanks for low prices. If you come from a family which celebrates Christmas, perhaps your parents or another relative would be willing to buy what you need for your turtles as a Christmas gift. Is it possible you could even get money for a vet visit this way?
You must also get a UVA/UVB light for your turtles. Not having one is a sentence to a slow death. They will get something called Metabolic Bone Disease (MBD). A Reptiglo 10 is a good brand of light. Don't take the word of a pet store emplyee that any other light provides both UVA and UVB. The words "full spectrum" also don't mean anything. The package must say that the light emits UVA and UVB. You can't count on sunlight through windows, because the glass blocks the rays. You can read more about lighting for turtles here:
Your basking area should be kept at 84 to 88 degrees. You can do this by moving the light down (make sure the turtles can't touch it) or by using a higher wattage light bulb. Put a thermometer there to be sure the temperature is not too cold or too hot. You can get a thermometer for under $2 in most pet stores.
Commercial turtle foods are a start toward a proper diet, but by themselves, they are inadequate. They should make up 1/4 of your turtles' diet. Another 1/4 should be animal products such as earthworms, canned cat food, bits of cooked chicken, etc. The remaining half of the diet should consist of fresh plant foods, such as leafy greens and bits of strawberry, melon, banana etc. For more complete information on feeding:
Now, for your sick turtle. The type of swimming you are seeing is often caused by a severe respiratory infection. Fluid accumulates in the lungs, making it impossible for the turtle to swim normally. Ear infections or abscesses can also cause unbalanced swimming. The white foam coming out of the mouth could also be the result of a respiratory infection, or it could be a symptom of stomatitis (mouth rot). The excessive shedding you saw to begin with is often a sign of some underlying infection brewing. These conditions are all serious. Treatment is likely to involve injections of antibiotics, or in the case of an ear abscess, surgery. Some experienced turtle keepers administer their own antibiotic injections, but it's difficult to calculate the proper doses, and easy to injure the turtle with the needle. The medications that are put in the water won't do any good for a turtle as sick as yours. I do have a few suggestions on how you may get help for your turtle. I'll give you a link in a moment to a directory of reptile vets. If Christmas money or a loan from your parents is not an option, you may be able to find a vet who will arrange a weekly or monthly payment schedule. The bill for the help your turtle needs is likely to be under $150. In some parts of the country, it would be much less, while in big cities, it may be more. Here's the link:
If you can't find a way to pay for the care your turtle needs, it might be best (for the turtle's sake) to surrender him to someone who can. If the turtle was caught in the wild, rather than being purchased in a pet store, a wildlife rehabilitator would be able to help him. This link will take you to a directory of rehabilitators:
If the turtle is from a pet store, there may be a reptile association with members who will help. If you'll tell me what state you live in, I can try to find such a group near you.
If your college has a biology department, you could pay a visit to one of the instructors to see if they know someone who may be able to help.
If you have further questions, just let me know. I hope you're able to quickly get help for your turtle.
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