Answer
The function is continuous when $a=-2.$
Work Step by Step
$\lim\limits_{x\to1^-}f(x)=3(1^-)^3=3.$
$\lim\limits_{x\to1^+}f(x)=a(1^+)+5=a+5.$
For the function to be continuous, $\lim\limits_{x\to1^+}f(x)=\lim\limits_{x\to1^-}f(x)\to$
$a+5=3\to a=-2.$
