Factorize:

We have:

$5 x^{2}-16 x-21$

We have to split $(-16)$ into two numbers such that their sum is $(-16)$ and their product is $(-105)$, i.e., $5 \times(-21)$.

Clearly, $(-21)+5=-16$ and $(-21) \times 5=-105$

$\therefore 5 x^{2}-16 x-21=5 x^{2}+5 x-21 x-21$

$=5 x(x+1)-21(x+1)$

$=(x+1)(5 x-21)$