If one root of the polynomial f(x) = 5x2 + 13x + k is reciprocal of the other,

If one zero of the polynomial $f(x)=5 x^{2}+13 x+k$ is reciprocal of the other. So $\beta=\frac{1}{\alpha} \Rightarrow \alpha \beta=1$

Now we have

$\alpha \times \beta=\frac{\text { Constant term }}{\text { Coefficient of } x^{2}}$

$=\frac{k}{5}$

Since $\alpha \beta=1$

Therefore we have

$\alpha \beta=\frac{k}{5}$

$1=\frac{k}{5}$

$\Rightarrow k=5$

Hence, the correct choice is (b)