Hello, I'm a mortgage professional.
I actually know Peekskill well as I mostly handle the lower NY area.
Yes, 5% does sound high with that credit score. I should be able to beat that.
The closing costs they would of given you probably include an escrow account. It's hard for me to tell if they are high without knowing more details but as far as the rate goes I'm certain I can beat that and save you some money.
We are a direct lender, we underwrite in 24-48 hours (that's fast) and I'm available almost 24/7.
If you have any questions or would like help with this you are welcome to contact me.