One idea is to let x/2 = p and y/5 = q, such that we get

p + q = 5 and
1/p + 1/q = 5/6.

Let's combine 1/p + 1/q into (q + p) / pq.

(q + p) / pq = 5/6

But p + q = 5.
5 / pq = 5/6
pq = 6

So,
p + q = 5
pq = 6

We can easily guess this to be 2 and 3, or the other way.

But you know how to do the proper way from here correct? Let you try on your own. Remember that we still need to find out the values of x and y, not just p and q.

There are many other ways to do this, including solving the x and y equations directly.

Thank you