Well, hopefully nothing is damaged, but those places aren’t known for using the best oil. One guy told me they just dump 30wt oil in whatever comes in – they don’t care what it uses. I thought he meant 5w30, but he said, “no, striaght 30wt!” my eyes got as big as golf balls.
I would use what the manual recommends. A 5w20 won’t hurt anything though. The 0w20 is just a little better flowing when the engine is cold – which might be beneficial to you in the winter time. I’m sure anything you get will be better than what they were using.