Solve the following recurrences. Assume $T(1)=(1).$

$($a$)T(n)=30T(\frac{n}{2})+n^5$

$($b$)T(n)=100T(\frac{n}{5})+n^2$

$($c$)T(n)=4T(\frac{n}{2})+n^2(logn{)}^3$

$($d$)T(n)=T(n-1)+n$

$($e$)T(n)=T(\frac{n}{4})+T(3\frac{n}{4})+n$

Note: Master Theorem may or may not be applicable in the above recurrences.