You say it works for 5 mins then doesn't again... does it work again immediately once you have restarted the car? Does it work again if you just leave the car running & turn the AC back on 10+ mins later?

Could be evaporator freezing up, system shutting down (via evap temp sensor or system pressure issues), thawing back out...

If you've tried changing the pump, I'm assuming it's not just low on refrigerant, as you'd have had it re-filled. Did you get it done properly, as you need to suck out all the air first.

Have you checked the appropriate fans come on with the aircon ?

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If at first you don't suck seed, try drier grain.

.....continued in a new thread of it's own to save confusion HERE