The first one

$\displaystyle 5p^4q - 20q^3 = 5q(p^4 - 4q^2)$ as mentioned above. But this can be factorised further.

$\displaystyle 5p^4q - 20q^3 = 5q(p^4 - 4q^2)$

$\displaystyle = 5q[(p^2)^2 - (2q)^2]$

$\displaystyle = 5q(p^2 + 2q)(p^2 - 2q)$

using the Difference of Two Squares rule.