everytime you refinance you spend closing costs, so if in 5 years again you refinance your spending more money to close on the loan. So even though rates for a fixed are at ~4% I would say stick with that. In 5 years they probably wont be that low and might even be around 7%. lock in at the fixed rate and start paying down the principal, the faster you get that down below 80% of initial loan value you can drop mortgage insurance and get out of escrow, which both cost you more.
I had everything figured out that if me and the wife could pay an extra 600$ towards debt a month we could have everything including the house paid off in just over 6 years. just my 2 cents
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