First house has a chance of 1/5. (1 mail is correct, you have 5 mails.)
Second house has a chance of 1/4. (1 mail is correct, you have 4 mails, only 4 since you have you already delivered the first house.)
Third house has a chance of 1/3.
Fourth house has a chance of 1/2.
Fifth house has a chance of 1/1.
What's 1/5*1/4*1/3*1/2*1/1?
=^._.^=