Help! My betta fish is lethargic!?

Everything looks good. The only thing I can think of is that the lights on 5 gallon tanks can really cause them to get hot during the day. 28-30 C is about 82- 84 F, if I did my conversion right, and that's a little high but the tank might be getting even warmer in the afternoon. I would check the tank temperature continuously during the day to make sure its not getting too hot. If it wasn't for the plants you could keep the lights off because betas don't need light. If the temperature is getting too high you can buy something to cool it down but it would be cheaper to get a bigger tank - more water takes more time to warm up. You can also use frozen water bottles but that will get tedious if you have to do it everyday. If you end up getting a bigger tank then I would get a shallow one - like a US ten gallon because betas are not strong swimmers.