Question 97057
let one number be x 
therefore the other number is 5*x

reciprocal of the first number {{{1/x}}}
reciprocal of the second number {{{1/5x}}}

given {{{1/x}}} + {{{1/5x}}} = {{{1/5}}}
multiplying by 5x on both sides we have 
{{{1/x}}}*5x + {{{1/5x}}}*5x = {{{1/5}}}*5x
5 + 1 =x
x=6 is one number.
the other number is 5x =5*6 =30

numbers are 6 and 30