Let’s solve the problem step by step. We’re given that the denominator is 5 greater than the numerator, and the sum of the numerator and the denominator is 13. We’ll use algebraic equations to represent the given information and find the fraction.

Let’s assume the numerator of the fraction is represented by ‘x’. Since the denominator is 5 greater than the numerator, we can express it as ‘x + 5’.

According to the problem, the sum of the numerator and the denominator is 13. This can be written as an equation:

x + (x + 5) = 13.

Simplifying the equation, we combine like terms:

2x + 5 = 13.

Next, we isolate the term with ‘x’ by subtracting 5 from both sides of the equation:

2x = 13 – 5,

2x = 8.

To solve for ‘x’, we divide both sides of the equation by 2:

x = 8 / 2,

x = 4.

We have found that the numerator, ‘x’, is equal to 4. To find the denominator, we substitute this value back into the expression ‘x + 5’:

Denominator = 4 + 5,

Denominator = 9.

Therefore, the fraction is 4/9.

In conclusion, when the numerator is 4 and the denominator is 9, the fraction is 4/9.