we have,

x-y is divisible by 5

say, x-y=5*k

where k be any integer.

x=5k+y................................................(i)

also we have

x = 29y+7

5k+y=29y+7 .............................from (i)

or, 28y=5k-7

or, y=(5k-7)/28............................(ii)

from (ii), it is clear that y will be integer only when (5k-7) is completely divisible by 28.

one of the possible cases is when k=7, then y=(35-7)/28=28/28=1

so, there are infinite number of possible integer values of y.

hence , y=1 is one of the possible values of y.