Determine the number of solutions of the equation $x_1+x_2+x_3+x_4+x_5=14$ in positive integers $x_1$, $x_2$, $x_3$, $x_4$, and $x_5$ not exceeding $5$.
I know I need to introduce a new variable, $y$, but then when I do that I get a negative...
$y_1=x_1-5$
$y_2=x_2-5$
$y_3=x_3-5$
$y_4=x_4-5$
$y_5=x_5-5$
my new equation would be $y_1+y_2+y_3+y_4+y_5=-11$