There are banks that will do 5-year fixed. Alternatively, if you pay off a 15-year mortgage as if it were a five-year fixed, with the extra money going to pay down principal, the cost isn't very different and you have more safety buffer. Talk to banks about options, or find a mortgage broker who'd be willing to research this for you.
Just to point out an alternative: refinancing at lower rate but without shortening the duration would lower your payments; investing the difference, even quite conservatively, is likely to produce more income than the loan would be costing you at today's rates. This is arguably the safest leveraged investment you'll ever have the opportunity to make.
(I compromised: I cut my term from 20 years to 15ish, lowered the interest rate to 3.5ish, and am continuing to let the loaned money sit in my investments and grow.)