Let's solve this problem step by step. We are given that a sum of N100.00 deposited for 5 years raises an interest of N7.50, and we are asked to find the interest rate.

The interest earned on a deposit is calculated using the formula `Interest = Principal * Rate * Time`, where `Principal` is the initial amount deposited, `Rate` is the interest rate per time period, and `Time` is the number of time periods for which the deposit is held. In this case, the interest earned is N7.50, the principal is N100.00, and the time is 5 years. We can use this information to solve for the interest rate:

Interest = Principal * Rate * Time

7.50 = 100 * Rate * 5

Rate = 7.50 / (100 * 5)

Rate = 0.015

Since interest rates are usually expressed as a percentage, we can convert this value to a percentage by multiplying by 100:

Rate = 0.015 * 100%

Rate = 1.5%

So, the interest rate at which a sum of N100.00 deposited for 5 years would raise an interest of N7.50 is **1.5%**. This corresponds to answer choice **C**.