The number of equivalence relations defined on set $A=\{a,e,i,o,u\}$ is $k$ then the sum of the digits in $k$ is 

1
1   2
2   3   5

5   7  10   15

15  20 27   37   52

52  67  87  114  151  203

In this triangle, the last number in the sixth row (203) represents the number of equivalence relations defined on a set with 6 - 1 = 5 elements.

Therefore the number of  equivalence relations $=52$

$\therefore x+y=7$