To solve this problem, we need to use the concept of proportionality in a work problem. We can use the formula for work done:

\[
\text{Work} = \text{Number of Boys} \times \text{Number of Days} \times \text{Earnings per Day per Boy}
\]

Given:
- 12 boys can earn N2,400 in 5 days.

First, calculate the earnings per day per boy:

\[
\text{Earnings per Day per Boy} = \frac{2400}{12 \times 5} = \frac{2400}{60} = 40
\]

Now, we need to find how many boys are needed to earn N4,200 in 21 days.

Let \( x \) be the number of boys required. The total work needed is:

\[
\text{Total Work} = 4200
\]

The total work in terms of \( x \) boys is:

\[
\text{Work} = x \times 21 \times 40
\]

Set the total work equal to N4,200:

\[
x \times 21 \times 40 = 4200
\]

Solve for \( x \):

\[
x \times 840 = 4200
\]
\[
x = \frac{4200}{840} = 5
\]


To earn N4,200 in 21 days, 5 boys are needed.

The correct answer is C. 5 boys.