The electric force between two point charges is given by Coulomb's law:

$$F = \frac{kq_1 q_2}{r^2},$$

where $$F$$ is the force between the charges in newtons, $$q_1$$ and $$q_2$$ are the magnitudes of the charges in coulombs, $$k$$ is Coulomb's constant (approximately 8.99 × 10⁹ N m²/C²), and $$r$$ is the distance between the charges in meters. In this problem, we have two electrons, which have a charge of approximately -1.60 × 10^-19 C. We are given that the force between them is 5.0 N. We want to find the distance between them.

Rearranging Coulomb's law, we get:

$$r = \sqrt{\frac{kq_1 q_2}{F}}.$$

Plugging in the values we know:

$$r = \sqrt{\frac{(8.99 \times 10^9 \text{ N m}^2/\text{C}^2)(-1.60 \times 10^{-19} \text{ C})^2}{5.0 \text{ N}}},$$

which gives:

$$r \approx 1.13 \times 10^{-10} \text{ m}.$$

Therefore, the two electrons are approximately 1.13 × 10^-10 meters apart.