re: Just put in my first application on a Mortgage

You've already been told some pretty accurate things. With your credit score where it is (biggest factor here, not your money down) and only 5% down, 5.25% is not terrible. It's also probably not the best you can do. I would also advise shopping around. And try to get away from big banks. Look local, look at brokers, etc. Don't let all of them do hard pulls on your credit. Talk to a lender, tell them your situation and have them give you a realistic idea of what you're looking at before authorizing any additional credit checks. Also, if there is any chance you can get your down payment up to 10%, ask about conventional 80/10/10 loan options. If you go FHA, you will NEVER be able to drop your PMI, even when you cross the 80/20 LTV ratio.

I would suggest checking with these folks: Triumph Home Loans

I shopped them recently and they beat the lender I used on my last purchase pretty handily with fewer fees. My FICO is higher than yours and I have a longer history, but I think you can do better than what you were quoted. You need to weigh out paying 5% down now and taking a 4.875-5.25% rate versus trying to accumulate a larger down payment and risking rates being in the 7s or 8s later on. It's a gamble. Keep in mind, people were talking about rates increasing for years before they ever actually did (a relative of mine got a 3.75% in 2013 and I did the same in 2016 while constantly hearing ads about how the rates were about to skyrocket), but since the ball has already started rolling, it's certainly plausible that things will trend upward faster.

Good luck.