TIMO 2017 - Senior Secondary (Grades 10-12) - Preliminary Round - Paper 5 Question 23

Integers $x_1,\ldots,x_5$ satisfy $x_1\ge-3$, $x_2\ge-2$, $x_3\ge-1$, and $x_4,x_5>0$. How many solutions satisfy $x_1+x_2+x_3+x_4+x_5=6$?