Let the sides of the $\Delta$le be $a=13,b=12,c=5$
Now $a^2=b^2+c^2$
$(13)^2=(12)^2+(5)^2$
Hence the Pythogrous theorem is true.
$\Rightarrow \angle A=90^{\large\circ}$
We know that $R=\large\frac{a}{2\sin A}$
$R=\large\frac{13}{2\sin 90}$
$\;\;\;=\large\frac{13}{2}$
Hence (b) is the correct option.