My turtle started with a 20 gallon tank and moved to a 55 gallon. Both tanks had heaters to keep the temp even. They also had basking and UVB bulbs.
I have not noticed any difference in appetite.
Turtles are cold blooded. Their metabolism is dependent on body temp.
5 gallons is too small in any case, but it can also lose / gain heat quickly. If I had to guess, I'd say your turtle is slowing down when it is cooler.
You should read the habitat recommendations on the main site:
http://www.redearslider.com/index_habitat.html