Let x be the number of 5 digit numbers sum of whose digits is even and y be the number of 5 digit numberssum of whose digits is odd, then
x=y
x+y = 90,000
x= 45,000
x < y
x =9 x 10 x 10 x 10 x 5 = 45000
Similarly y= 45,000
x = y & x+y= 90,000