I'm just going to reiterate what has already been said, he has no appetite and is lethargic because:
#1.) Your
UVB bulb is totally inadequate for a bearded dragon, it's only a 13 watt bulb. While you do want a Reptisun 10.0
UVB light, it absolutely must be at least an 18" 10.0 tube
UVB light in a matching length tube fixture that has a reflector behind it. It also MUST be mounted under that mesh lid, as it is blocking up to 50% of the already way too weak
UVB light for a beardie. It also must be withing 6" of his basking spot if it is an 18" Reptisun 10.0 T8 UVB tube, which is the weaker strength tube, and the 10.0 T8 UVB tube must be replaced like clockwork every 6 months. If you order on Amazon.com, the 16" or 22" Reptisun 10.0 (NEVER USE A 5.0 OR 2.0) T5 High-Output UVB tube is a much better UVB tube for a bearded dragon, and you can actually get a package deal on Amazon for a 22" Reptisun 10.0 T5HO UVB Tube and the matching length fixture that is rated for a T5HO tube and has a reflector built in. The T5HO can sit on top of the mesh as it is strong enough to penetrate the mesh, but still must be within at least 11" of his basking spot. The 10.0 T5HO UVB tube must be replaced like clockwork once a year. Just an FYI, UVB tubes stop emitting any
UVB light at all at these ages, even though the tubes are not burnt out and still light up. ALSO, HIS BRIGHT WHITE BASKING LIGHT AND UVB TUBE MUST BOTH BE ON FOR AT LEAST 14 HOURS EVERY SINGLE DAY FOR A BEARDED DRAGON.
Buying him a proper 10.0 UVB tube is not optional, obviously, because without it he will not have any appetite, he will not be able to manufacture any vitamin D3 on his own, will not absorb and calcium he is eating, and he will be stunted in growth and develop MBD. So please get him an appropriate UVB tube immediately.
#2) His temperature zones are FAR TOO LOW and this will also cause extreme lethargy and lack of appetite, and will also not allow him to process his food. You cannot use that stick-on thermometer, as already mentioned they are off by up to 20 degrees if tested, and in addition you have absolutely no way to measure his Basking Spot Temperature with one. You need to spend $10 at Petco or PetSmart on a digital thermometer with a probe on a wire. These are accurate, and you can set the probe right on his basking spot to get the surface temperature. This all being said, you cannot keep him in a 5 gallon tank, nor a 10 gallon tank, as bearded dragons absolutely must have a temperature gradient going across their tanks, and at a minimum you need a 20 gallon long tank to be able to get any kind of temperature gradient. And a 20 gallon long tank will only be large enough for him until he's about 4-5 months old, after that a minimum size is a 40 gallon breeder tank, and for an adult of 2 years and older this is also too small. Most people start their babies in a 40 gallon breeder tank and then go to a custom tank for adults, a minimum of 4'x2'x2'. For now though, you need at least a 20 gallon long, but this is pointless because in a couple of months it will be too small, so you should just go and buy a 40 gallon breeder tank now, check Craigslist, they are usually all over the place.
To show you how far your temperatures are off (and they are actually off by more than this as your thermometer is no doubt off by between 10-20 degrees), his Main Basking Spot on the Hot Side of the tank should be between 105-110 degrees for a baby/juvenile, and around a year old they tend to like it a bit lower, between 100-105 degrees. This is not optional. The only way to measure this is to buy the digital probe thermometer, let the probe sit on the main basking spot for at least 20-30 minutes, then read the temperature. His Hot Side Ambient temperature should be between 88-93 degrees, and you can just put the probe on the floor of the Hot Side of the tank, or attach the suction cup they have to the side of the tank, and again you must let it sit for 20-30 minutes before reading the temperature. The Cool Side Ambient needs to be between 75-80 degrees maximum, as he must always have a Cool Side that is considerably cooler than the Hot Side Ambient to go to. So you can see why the small tanks will not work for him at all. It's impossible to get his temperatures correct in anything smaller than a 40 gallon breeder tank for a bearded dragon, and they are desert reptiles so obviously this is a big deal, just as big as having an adequate, long 10.0 UVB tube that is mounted correctly. Without making these changes he will not have any appetite and will be lethargic.
Also, no more medication, and please do not go back to that vet. That was a horrible medication to give a little baby bearded dragon for parasites that were not tested for, and not only that, that medication is only appropriate for 2 strains of coccidia that are rare. It's a harsh medication that only compounded his issues. The vet should have asked you about what
UVB light you were using and what your temperatures were, that would have told him what the problem was.