Refinance and Rent Vs Sell and move on?

[Chris Jones]

Here is yet another one of these questions, thanks in advance for your guys help.

I have a home that I purchased for my primary residence close to 5 years ago.  I put 20% down on the property at purchase and got a 30yr fixed rate mortgage at 4.875%.  I have been offered a job in another city 1700 miles away and was planning on selling the house in May when I transfer.  

This winter in the rainy climate where I live I ended up with a leak in my roof.  Previous owner put the roof on himself and you guessed it, he screwed it up. So now we need a new roof.  Estimates for a new roof are between $5,500 and $7,000.  

I have considered refinancing the mortgage into a 15yr fixed rate with an interest rate near 3.5% and renting the property out instead of selling to help recoup the costs on the roof.  A 15 yr mortgage will rapidly accelerate paying down the principal on the mortgage.  

Here's the numbers

Home valued at $205,000 purchased 4 and a half years ago for $190,000 with 20% down payment.

Current mortgage $138,000 remaining balance at 4.875% interest with 25 and a half years left.  Current payment including property taxes and insurance is $1,090/month.

Rent estimate for the property is $1300 per month.  3 bedroom 2 bath single family home with attached garage in nice neighborhood with good schools and great location for highway access.

Refinancing to a 15yr mortgage would add an estimated $175/month to the total payment.

I don't need the equity in the property right away when I get to the new city as I plan to rent for roughly 2 years to see if I will stay.

My estimates put the total principal pay off over 5 years at close to $40k with a 15yr mortgage and only $15k with a 30yr.

So should I rent the house and refinance or sell and move on?