Let r be the number of houses to the right of my house
and l the number of houses to the left of my house when I look toward
the river. We have the following simultaneous equations:

r + l = 10
rl - (r+1)(l-1) = 5

Hence, r + l = 10 and r - l = 4.

thus r = 7 and l = 3.

My house is therefore the fourth from the left when facing the river.