.
Consider this: There are $\displaystyle \binom{5}{3}$ ways to select the rows for the three rooks.
Now order the rows from least to most.
There are five ways to place a rook on the least numbered row.
There are four ways to place a rook on the next numbered row in a non-attacking position.
There are three ways to place a rook on the last numbered row in a non-attacking position.