A fraction becomes  when 1 is added to each numerator and denominator. However, if we subtracted 5 from each, then it becomes . The fraction is :

The problem is asking to find a fraction which satisfies two conditions:

1. When 1 is added to both the numerator and the denominator, the fraction becomes 1/2.
2. When 5 is subtracted from both the numerator and the denominator, the fraction becomes 1/3.

Let's denote the numerator as x and the denominator as y.

From the first condition, we can write the equation as (x+1)/(y+1) = 1/2.

From the second condition, we can write the equation as (x-5)/(y-5) = 1/3.

Now we have a system of two equations:

1. 2x + 2 = y + 1
2. 3x - 15 = y - 5

Solving these equations simultaneously, we find that x = 7 and y = 8.

Therefore, the fraction is 7/8.