Most leases are for one year. Some are for two. Very few residential leases are for five years.
If you mean the mortgage is only for 5 years--rather than for 15 or 30--contact another lender or mortgage broker. A 5-year mortgage probably has a balloon payment at the end. Your payments are the same as if you had a 30-year lease, but at the end of the 5 years you have to refinance. A lot of people lost their homes maybe 3-5 years ago with just that type of mortgage, when they discovered they were unable to refinance.
Check with a lender or mortgage broker for more information.
Hope that helps.