To an extent, rabbits as well as other pets adapt to our active hours. They are crepuscular, which means they are the most active at dawn and dusk. 5.30 is pretty much dawn. They will nap during the day – my bun is 7.5 months now and if I’m at home, I barely hear a sound from her during the day, unless I try to eat an apple, in which case she suddenly appears by my feet, almost like magic.
My bun sleeps through the night. She sits in her litterbox and eats hay when I go to bed, (the best sound to fall asleep to!) but she doesn’t really consume any hay during the night, but she does start eating as soon as Im up and about.
If your bun goes through a good amount of hay per 24 hours and if his poops are good and plentiful, I dont think you have anything to worry about. You can weigh him once per week and keep a weight diary so you see that he’s gaining like he should – at his age, he should still be gaining some weight, although nothing dramatic.