Given Information:
- Denominator exceeds numerator by 2.
- Adding 5 to the numerator increases the fraction by unity.

To find the fraction, we can use the following steps:

Step 1: Let's assume the numerator of the fraction to be x. Then, the denominator will be x + 2 (as per the given information).

Step 2: Using the assumed values, we can write the fraction as x/(x+2).

Step 3: As per the second condition, adding 5 to the numerator will increase the fraction by unity. "Unity" means the fraction will become 1 (i.e., the numerator and denominator will be equal). So, we can write the following equation:

x+5 / (x+2) = 1

Step 4: Solving this equation, we get:

x+5 = x+2
3 = 0

This is not possible. So, our assumed values are incorrect.

Step 5: Let's try another assumption. Let's assume the denominator of the fraction to be x. Then, the numerator will be x - 2 (as per the given information).

Step 6: Using the new assumption, we can write the fraction as (x-2)/x.

Step 7: Using the second condition, we can write the following equation:

(x-2+5)/x = (x+3)/x = 1

Step 8: Solving this equation, we get:

x+3 = x
3 = 0

This is not possible. So, our assumption is incorrect.

Step 9: Let's try one more assumption. Let's assume the numerator of the fraction to be x and the denominator to be x + 2 (as per the given information).

Step 10: Using the new assumption, we can write the fraction as x/(x+2).

Step 11: Using the second condition, we can write the following equation:

(x+5)/(x+2) = x/(x+2) + 1

Step 12: Solving this equation, we get:

x+5 = x+2 + x+2
x = 3

Step 13: Using x = 3 in the fraction, we get:

3/(3+2) = 3/5

Therefore, the fraction is 3/5, which is option D.