5000 lb is not a pressure it is a force so the question as asked makes no sense.
Even if the 5000 lb was distributed optimally over the top of the box, 5000 lb is a very high load for plastics although I GUESS this box has quite thick walls so the load MIGHT be spread over a large area.
It is difficult to mould plastics with very thick walls and their properties are diminished when it is to thick. Thinner wall and ribs can be used, but that leads back to load vs bearing area problems again.
If it is reasonably concentrated in the centre it has no chance of survival at all. It even takes a reasonably substantial steel structure to take a 5000 lb load in the middle of a 3' span.
A box with very high structural integrity made from thermoplastic would need to be injection moulded and would made from a very strong material like 50% glass fibre reinforced nylon or PET.
Just the steel to make a mould that large will probably cost as much as your house. The final mould will be a block of steel about 11'by over 4'by over 4'. Say 220 cubic foot of steel. Steel has an SG of a bit over 7. My rough calcs say that is a bit over 40 tonne if I counted the zeros correctly and got my off the top of the head conversion factors right.
As it composes a core and cavity, that is about 70 tonne of tool steel and a few tonnes of mild steel to make the mould.
Add to that many hundreds of hours of machine time at a very specialized toolmakers.
Add to that transport and handling costs on a mould that heavy.
Add to that the hourly rate divided by the cycle time in one of the largest moulding machines in the world.
Also, material used will be 2 sides at 90 by 34, plus 2 sides at 90 by 32 plus 2 sides at 34 by 32 at say 3/8"thick, with substantial reinforcing ribs at say 30% increase in volume over no ribs with a material SG of say 1.5. Say 350 pounds per shot at say $2 per pound say $700 per shot.
If that is feasible you still seriously need to employ someone who at least knows how to do a ballpark design then recost based on more than wild guesses.
Regards
Pat
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