Let the first number be x.
The second number will thus be x + 1, since the two numbers are consecutive.
3/4 of the first number will be (3 / 4)x = 3x / 4
1/2 of the second number will be (1 / 2)(x + 1) = (x + 1) / 2
Since 3/4 of the first number is 5 more than 1/2 of the second number, we have:
(3x / 4) - ((x + 1) / 2) = 5
(3x / 4) - (2(x + 1) / 4) = 5
(3x - 2(x + 1)) / 4 = 5
(3x - 2x - 2) = 4 * 5
(x - 2) = 20
x = 20 + 2
x = 22
Hence, the first number is 22 and the second number is 23.