One positive integer is five more than the other. when the reciprocal of the larger is subtracted from the reciprocal of the smaller the result is 5/14. find the two integersif you could, show me the steps so that i will know how to solve a problem similar to this one in the future.

Let x be a first positive integer number, the second number is 5 more then x and you can write that the second number is x+5.
The recipracals of numbers x and x+5 are and , respectively. Since x<x+5, then and 
.
To solve this equation you have to find common denominator:


, then
and

and solutions are
and . 
Since x is positive integer, the right solution is x=2 and incorrect x=-7.
x=2, x+5=7