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Converting both sides to decimal,

6x+5 = 5y+2

We get, 5y - 6x = 3

Now, the first number has 5 and 6 as its digits. So x is definitely greater than 6. The second number has 5 and 2 as its digits. So, y is definitely greater than 5.

So, x can be 7,8,9,10..... and y can be 6,7,8,9.....

By inspection, if we take y as 9 and x as 7, then the equation is satisfied.

So, minimum value of (x+y) should be 16.

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we know that x>6 and y>5

     6x+5=5y+2

=>   6x+3=5y

=>   3(2x+1)=5y

=>  2x+1 is divisible by 5 and is odd at the same time x>6

so minimum value possible for 2x+1 is 15

which gives x=7

=>from solving above equation we get y=9.

So minimum value of x+y is 7+9=16
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