Let's solve the problem step by step:

1. Determine Bola's original share:
- The ratio of Bola's and Tolu's shares is 5:8.
- The total value of the business is ₦1,300,000.
- The total ratio is \(5 + 8 = 13\).

Bola's original share is:
\[
\text{Bola's share} = \frac{5}{13} \times 1,300,000 = \frac{6,500,000}{13} = ₦500,000
\]

2. Calculate 20% of Bola's share:
- Bola is selling 20% of her share to Tolu.
\[
20\% \text{ of } ₦500,000 = \frac{20}{100} \times 500,000 = ₦100,000
\]

3. Determine Bola's new share after selling 20%:
\[
\text{Bola's new share} = ₦500,000 - ₦100,000 = ₦400,000
\]

So, after selling 20% of her share to Tolu, Bola would own ₦400,000 of the business.

The correct answer is A. ₦400,000.