It is given that $p = \dfrac{q + r^2}{q - 5}$.

1. Substitute $q=\dfrac15$ and $r=-6$ into the formula and evaluate.

$p=\dfrac{q+r^2}{q-5}$

$=\dfrac{\dfrac15+(-6)^2}{\dfrac15-5}$

$=\dfrac{\dfrac15+36}{\dfrac15-5}$

$=\dfrac{\dfrac{181}{5}}{-\dfrac{24}{5}}$

$=-\dfrac{181}{24}$

1. Clear the denominator by multiplying both sides by $q-5$.

$p=\dfrac{q+r^2}{q-5}$

$p(q-5)=q+r^2$

2. Collect the terms involving $q$ and factorise to isolate $q$.

$pq-5p=q+r^2$

$pq-q=r^2+5p$

$q(p-1)=r^2+5p$

$q=\dfrac{r^2+5p}{p-1}$