jmc

Because the three points are on the same line, the slope between the first and second equals the slope between the first and the third. This gives us the equation: $$\begin{array}{rl}\frac{3-(-5)}{(-a+2)-3}& =\frac{2-(-5)}{(2a+3)-3}\\ \frac{8}{-a-1}& =\frac{7}{2a}\\ 8(2a)& =7(-a-1)\\ 23a& =-7\\ & a=\boxed{\frac{-7}{23}}.\end{array}$$