Answer
$(x+2)(5x+12)$.
Work Step by Step
The given expression is
$=5(x+1)^{2}+12(x+1)+7$
Substitute $x+1=u$.
$=5(u)^2+12u+7$
Simplify.
$=5u^2+12u+7$
Rewrite $12u$ as $5u+7u$.
$=5u^2+5u+7u+7$
Factor.
$=5u(u+1)+7(u+1)$
$=(u+1)(5u+7)$.
Substitute back $u=x+1$.
$=((x+1)+1)(5(x+1)+7)$.
Simplify.
$=(x+1+1)(5x+5+7)$.
$=(x+2)(5x+12)$.