Let the integers be x, x+2, x+4. If the first and third of three consecutive odd integers are added, the result is 69 less than five times the second integer. So, 

x+x+4 = 5(x+2)-69.

2x +4 = 5x +10-69 = 5x -59.

3x = 59+4 = 63.

x = 63/3 = 21.

So, the numbers are: 21, 23, 25