We need to find out how many hours it will take for 7 persons to paint 7 walls of equal area, given that 5 persons can paint 5 walls in 5 hours.

Let's break down the given scenario:

1. Initial Rate of Work: Here, we are told that 5 persons take 5 hours to paint 5 walls. This means that the \(5\) persons are working together and they complete \(5\) walls in \(5\) hours.
2. From this, we can deduce that:

\(\text{Rate of work per person} = \frac{\text{Total number of walls}}{\text{Number of persons} \times \text{Number of hours}} = \frac{5 \text{ walls}}{5 \text{ persons} \times 5 \text{ hours}} = \frac{1}{5} \text{ (walls per person per hour) }\)

1. New Scenario: Now, we want to calculate how long it takes for 7 persons to paint 7 walls.
2. Since each person paints \(\frac{1}{5}\) wall per hour, 7 persons will paint walls at the rate of:

\(\text{Total rate for 7 persons} = 7 \times \frac{1}{5} = \frac{7}{5} \text{ walls per hour}\)

1. The total number of walls to be painted is 7. Therefore, the time required for 7 persons to paint 7 walls is given by:

\(\text{Time} = \frac{\text{Total number of walls}}{\text{Total rate}} = \frac{7}{\frac{7}{5}} = 5 \text{ hours}\)

Thus, the required time for 7 persons to paint 7 walls is 5 hours.

The correct option is 5.