Ways up five stairs in steps of one or two

A staircase has $5$ steps, and each stride covers either one step or two. In how many distinct sequences of strides can you reach the top?

8. The last stride comes from one or two steps below, so $f(n)=f(n-1)+f(n-2)$ with $f(1)=1$, $f(2)=2$. This gives $3,5,8$ for $n=3,4,5$.