\[3ab^{2}(4a - b) - 20ab + 5b^{2} =\]
\[= 3a^{2}b(4a - b) - 5b(4a - b) =\]
\[= (4a - b)\left( 3a^{2}b - 5b \right) =\]
\[= b(4a - b)(3a^{2} - 5)\]