Question:

Let $f^1(x) = \dfrac{3x+2}{2x+3}$, $x \in \mathbb{R} - \left\{-\dfrac{3}{2}\right\}$. For $n \ge 2$, define $f^n(x) = f^1 \circ f^{n-1}(x)$. If $f^5(x) = \dfrac{ax+b}{bx+a}$, $\gcd(a,b)=1$, then $a+b$ is equal to ______.