I have an AC in my garage for a room built inside with about 5 feet of space between the garage walls
And the room walls. It gets really really hot in that 5 foot space. My question is will the AC burn out
Or should I build a box around it to vent outside which during the summer is almost as hot but at night
The garage stays hot.

Are you referring to an air handler on a split system that is in the garage? If so than you should have no issues as long as the return and supply are well ducted and insulated. We have many air handlers vertically mounted in garages in AZ and our garages get muy caliente.

The unit is a regular window AC. Its on a stand in the 5 ft space of the garage. It cools fine into the room but its so hot in the area surrounding the room I'm afraid it can't be good. The garage has its own 240v supply which the AC is wired to.

Ok got it, so the air in the conditioned room is being recirculated by the 'window shaker' and that does not care. The refrigerant that travels through the system does care because it moves the heat from the evaporator to the condenser and that is expelled out into the garage via the fan motor. The condenser is recirculating air in the garage - pulling it across the condenser coil and expelling very hot air back into the garage. vicious cycle.

This would cause higher pressures and temperatures in the compressor/condenser and load on the motors. How much? Tough to tell. You will know when it has had enough because the indoor cool air will start to slowly warm up as it looses efficiency.

Is it worth building a vent to pull outdoor air in to the condenser and then expel that to the garage. Tough call but for the cost of a window unit I would probably say no.

If you ever decide to upgrade later there are some mini-splits, we call them, ductless and would probably work great in your situation.

Good luck.

Where does the condensate water drain? AC needs to be on outside wall for efficient cooling and drainage.

Okay.. I have an apartment size ac.. it does not fit in any windows.. so I pluged iit on my sink for today cause it will be 40 c outside today and my son has asthma am I safe to do this

The back of the unit must vent outside.