Answer
-$\frac{13}{5}$
Work Step by Step
Let's assume that reciprocal of -$\frac{5}{13}$ is '$ x$'.
By definition, product of a number and its reciprocal is always 1. Therefore-
$ -(\frac{5}{13})\times x $ = 1
$x$ = $\frac{1}{-(\frac{5}{13})}$
or $ x$ = -$\frac{13}{5}$
i.e. reciprocal of -$\frac{5}{13}$ is -$\frac{13}{5}$
