The reciprocal of a number refers to the inverse.
In this case, first, we transform -5 3/1 into a fraction.
[tex]-5\frac{3}{1}=-\frac{5\cdot1+3}{1}=-8[/tex]As you can observe, the number is -8, its reciprocal would be its inverse number.
[tex]-\frac{1}{8}[/tex]