z = a + ib

|a+ib-5i| = |a+ib+5i|

|a+ib-5i|² = |a+ib+5i|²

|a +i(b-5)|² = |a + i(b+5)|²

a²+(b-5)² = a²+(b+5)²

a²+b²+25-10b = a²+b²+25+10b

20b = 0

b = 0

b is a imaginary part of z

= y

= 0

Im (z) = 0

So, the locus point is real axis