I'm confused as to why if he is 3mo he's getting such a mix of things in his bottle? I'd start there. If there is no reason (like Dr rec) for him to have rice cereal in his bottle I'd stop using it. At 3mo babies should still be on only breastmilk or formula.
If you are giving him 100% BM then know that BFed babies get hungry more often then ones on 100% formula. Also-depending on how big a baby he is he may be hungry for more then 5pz at a bottle.
Also though-he is still to young to be expected to sleep on really long stretches-but he's on the cusp on devloping his sleep pattern for long term. It's up to you to help get him on track with his sleep however.
Do you swaddle him when he sleeps? That will help too.
I would try a few things....
-Change his bottle to all BM or all Formula and increase to 6oz
-Be sure you're burping him mid-way thru the bottle
-Swaddle when he's sleeping
-Start getting him on a sleep schedule-for example let's say he wakes up at 6am: Bottle
he might be up for 1-2 hours, maybe three....starts getting sleepy about 8ish-bottle/nap
Sleeps for about 1-2 hours, wakes....bottle. Play/interact/etc up for 2-3 hours, bottle/nap...it will go on like that all day, until about 6pm you want to start your wind down and make it obvious that it's nighttime and it's different than just a nap
bath, pj's, snuggle, bottle, rock, swaddle, down for the night---which may only be 4-5 hours, but increases over time. and Repeat. :)
At 3 mon he won't be sleeping thru the night (8-10 hours), but he should be starting to sleep in longer stretches at night-4+ hours...BUT during the day his naps should be shorter - less then 3 hours at a time.