Value for a variable as a rational number

Question

Given that $a$ and $b$ are rational numbers and that $x = \frac{\sqrt 5+3}{\sqrt 5+2}$ is the solution for $x^2 + ax + b = 0$

Can I derive the values of a and b from the resulting equation? $$ -a + b + 6 + (a - 2)√5 = 0 $$