be a function defined as

Let $f(x)$ is continuous at $x=1$, then

$f\left(1^{-}\right)=f(1)=f\left(1^{+}\right)$

$\Rightarrow \quad 5=a+b$ ..........(1)

Let $f(x)$ is continuous at $x=3$, then

$f\left(3^{-}\right)=f(3)=f\left(3^{+}\right)$

$\Rightarrow \quad a+3 b=b+15$...........(2)

Let $f(x)$ is continuous at $x=5$, then

$f\left(5^{-}\right)=f(5)=f\left(5^{+}\right)$

$\Rightarrow \quad b+25=30$

$\Rightarrow b=30-25=5$

From (1), $a=0$

But $a=0, b=5$ do not satisfy equation (2)

Hence, $f(x)$ is not continuous for any values of $a$ and $b$