The appraisal our bank did came in $5000 higher than our purchase price, is that good?

This is definitely a good deal for you, since the appraisal exceed the sale price you now have $5000 equity in your new house purchase. There are some clauses in sales contracts that would indicate the appraised value would be the sale price. I hope this is not the case in your transaction.

I hope this has been of some benefit to you, good luck.

"FIGHT ON"

Its fine, it means your can get the loan you want. You can get the loan on the lesser of the appraised price or sales price so this doesn't increase the loan amount you can get, but at least the appraiser thinks its a good deal and you the appraisal won't hold up the closing.

It's good. You paid less than what it was worth, and that's always a good thing.