Looking to refinance my house to 15yr need some suggestions

Quick excel amortization schedule:
$51k @ 5% for the remaining 27 years = $42,000 in interest with a payment of $287/month

$51k @ 3% for 15 years = $12,395 in interest and a total payment of $352 (not including closing costs).

Now, $51k @ 5% for 27 years + extra principle payment of $65 a month = $27,333 in interest, saving $14,400 and paying it off over 8 years early.

Now, apply the what, $5,000 in closing costs? to the principle now instead, and apply the extra $65/month, and you get a total Interest paid of $20,600, and reduce the time by over 11 years (payoff by 09/2028 (15.8 years from now).

Refinancing may not be a bad deal in the long run.

You would need to increase your current monthly payment by almost $300 extra to equal the amount saved vs a 15 year fixed at 3%.