Question 80893
there are two solutions
name your number x, then reciprocal is 1/x
so x+4/x=-5
find common denominator 
{{{(x^2+4)/x=-5}}} cross multiply
{{{x^2+4=-5x}}}
{{{x^2+5x+4=0}}} you can factor this equation into
(x+4)(x+1)=0 thus, x+4=0 and x+1=0
so your two solutions are
x=-4 and x=-1

good luck