It really depends on the horse, but I have always liked the (spiral) leg-yield to the wall and leg-yield out on a circle exercise to get a green horse’s hind end engaged.
The added bonus being, this usually is the prerequisite to teaching shoulder-in. I’m assuming real lateral work he does not quite know yet, if he is 5 and in an H/J barn - but that doesn’t mean he can’t do leg yields, and start to learn shoulder-in.
Five is too young for collection in most horses - if you are following the traditional german training scale, Collection is the last piece of the puzzle, top part of the pyramid, and clicks into place once the other “parts” are all assembled.
It sounds as if you are worrying a bit too much about his head, just from the way you describe the difficulties you’re having.
Pole work is another good way to strengthen the hind end - in some ways I like it better than lateral work in a young horse - but both are excellent tools.
An exercise I use more commonly, when I’m trying to get the green TBs to really “sit back and step under”, or at least understand the concept –
Pick up trot, 20m circle
Leg yield into the circle, gradually spiraling in on a leg-yield until it is as small as you can get them to do, without them becoming stiff or unbalanced or above the bit
Leg yield back out to the circle gradually - at first, it may take you a full circle or two, that is ok
On the last segment of the circle, pick up a canter
Leg yield spiral out, until horse is on the wall
Canter long side
Trot short side
Trot 20m
Rinse and repeat
As the horse begins to understand the exercise, throw in other “within the gait” transitions - medium canter down long side, working canter short side, working trot transition, etc.
The canter long side, is usually to give them a mental “break” before back to the spiraling in - you don’t want to drill, but you don’t want to be inconsistent, either. Look for rhythm and balance on the long-side, and suppleness around the turns.
One other thing, to consider in this big picture puzzle – if the horse is becoming gradually heavy, either to the hand or on the forehand, it sometimes can be a symptom they are tired or not quite fit enough for the level of work they are doing, or, it may be something physical blocking them from using their back and stepping under.