Answer
Yes
Work Step by Step
Find the angular resolution using equation 25–7.
$$\theta=\frac{1.22\lambda}{D}$$
The smallest feature resolvable, L, is that angle multiplied by the distance to the Earth from Mars, r.
$$L=r \theta=\frac{1.22 r \lambda}{D}$$
$$=1.22 \frac{(8\times10^{10}m)(550\times10^{-9}m)}{0.005m}$$
$$ = 1.07\times10^7m$$
This is considerably less than the distance between the Earth and its moon, so a person on Mars would be able to resolve the Earth and its moon as separate objects without using a telescope.