I need help please!!!!!!!!!!

Hello!
I just brought home a baby Savannah, and I have some concerns.

'Loki' looked very healthy when we brought him home, and he was eating well. BUT: He sleeps a lot, temps and humidity are where they are supposed to be in each spot, and he does go into his water dish, and hang out.
Today, I put in two crickets to start, and he isn't paying attention to them...one crawled right under his nose.

I am just trying to keep this little one healthy and alive. Is there anyone who can give me some tips?

I know you said that temperature and humidity are where they are supposed to be...but, since I don't know where you got your information OR anything about the set up you have, please describe: what type of enclosure it is in. how you are providing heat. how, where, and when you are measuring temperature (type of thermometer(s) you are using, location(s), etc. what are the day/night, the warm/cool, and high/low temperatures. what are the humidity levels. room temperature.
Also, are you handling him? Is the enclosure near a window, fan, air conditioner? Are you using supplemental lighting?

Okay!
Day is around 89 degrees, night is around 79. There may be a one or two degree differential. On top of his basking spot is about 100 degrees.

Loki is in a 5 gallon tank, at the moment, as his enclosure is being built. We were told that this is acceptable, as he is only about 5 inches from nose to tip of tail. The tank is not located near any windows or doors or vents.

We have two thermometers, one on each side. Humidity is around 70, and he has several shady areas and hides.

He eats okay, but he does seem to sleep a lot. I don't know my room temperature, but it is fairly average, no A/C on, just a fan in the room adjoining the one we have him in, when needed.

He has the 'full spectrum' light on, 10 hours a day. It goes off at night, and the temperature and humidity stay at what I was informed are acceptable levels, which I mentioned above. Only his basking spot lowers dramatically after the light is off, but he is sleeping at that time, and doesn't go up there.

I do handle him, once or twice a day, for a few minutes, and he seems fine. I always wash my hands before and after. I am very paranoid about these things.

After I wrote, I took out the crickets, placing them back in again in about 3 hours, he did eat them then. Right now he is sleeping in a hollow in his log.

His substrate is misted a little each morning, as I was told to do by a Sav owner I know.
We use a bark for him, and I have cleaned it out already, even though he mostly uses his water dish as a toilet, as I was also informed was normal. I rinse that every time he uses it for that purpose.

Please let me know if anything is wrong with what we are doing.

The problem with a 5 gal tank is that it is hard to regulate temperatures, but the ones you have listed are basically ok (a slightly warmer basking area is usually recommended for savannahs, but your's will work for now. The only things I will contradict are the humidity level, and the practice of misting his bark. Savannahs do not require that much humidity, and it can become problematic for them. Also, I understand that lights dry out bark substrate (any substrate, lol), but savannahs are susceptible to fungal infections on their feet/toes when kept in high humidity and/or too moist substrate (kind of like athletes foot, except their toes will fall off, lol). If you have a water bowl big enough that he can crawl into it, as you referenced, that is sufficient.

Thank you very much for your advice!!!

What would you suggest as a preferable humidity level?
I am so attached to this little guy, and I want so much for him to flourish into the healthy adult I know he can be!!!

do your best to get him out of that tank asap, BUT keep in mind that when you move him to a larger enclosure if it's too big it will stress him out just as much as too small of an enclosure. So if you build a huge cage, make sure you partition it off into sections until he grows to the appropriate size, good luck