Hi, if u have to feed him at 5am, use a timer to get his lights to come on at 4am if it doesn't 'cause too much interruption in the home, that way he's more active n ready to eat, or feed him veg of a morning, insects afternoon (Chris has it right). Just then make sure he's getting a good 8-10hrs no lights of a night time. They're flexible to your lifestyle if need be.
You could also bump up your heat temps so it's at 40-44C thruout the day, not just middle of day - what wattage heat bulb u got for the size enclosure?? Also what uvb u using & how far from the basking spot? As long as there's a cool area of 28C approx then all good.
Heat is the most important factor in them being able to digest their food first & foremost, uvb then aids in them absorbing the calcium/vitamins from the digested food.
Re the meal/superworm suggestion, until u get him pooing on a more regular basis, I'd (as James suggested) give them a miss - if your heat isn't up to scratch, they're one of the biggest impaction threats to beardies.
If your heat, uv, diet etc is correct, the absolute norm is everyday pooing, with the occassional one going a day or 2.
Last question - have u got a water bowl in his enclosure for him to soak in naturally if needed??