Combinatorics:No of solutions to an equation

Question

Find the number of solutions to the equation $x_1 + x_2 + x_3 + x_4 + x_5 = 22$, where $x_1, x_2, x_3, x_4$ and $x_5$ are non-negative integers, and $x_1+x_2 \leq 2$. (You may leave the answer as an expression consisting of binomial coefficients.) So I tried solving it and I think we need to consider the cases when $x_1+x_2$ is equal to $2$; when $x_1+x_2$ is equal to $1$ and so on.