is it better for growth to pinch off some eggplant growth or let a quantity grow on the one plant? this plant has 5

They and the plant look fine - magnificent, actually - to me. I'm no expert, of course; mine never have more than three fruits.

I have a lot of eggplants, eating them non stop starting begging of July, but my plants are 5-6' tall and bushy.
Loretta, yours look great, what kind are they? Looks perfect height and some of them look ready to harvest. Just thinking that need some low highs for the next season.

Loretta, I suppose its a judgement call, if the plant seems healthy enough and big enough to support, let them grow.
My plants were scrawny and pitiful this year, managed to set a few fruit. Even very small, they seemed ok cut up in tomato sauce.
Do watch and use the eggplants when big enough; would be a shame and stress the plant unnecessarily to leave them too long past prime.

Two of those guys look about ready for moussaka.