Answer
$\mathrm{F}_{1} \lt F_{2} \lt F_{4} \lt F_{3} \lt F_{5}$.
Work Step by Step
A spherical distribution of charge, when viewed from outside, behaves the same as an equivalent point charge at the center of the sphere. A charge inside the sphere experiences no force.
So, we use Coulomb's law with Q acting as a point charge:$\quad F=k\displaystyle \frac{Qq}{\mathrm{d}^{2}}$,
$F_{1}=0,\ \quad$ (inside the sphere)
$F_{2}=k\displaystyle \frac{Q(2q)}{(3\mathrm{d})^{2}}=\frac{2}{9}F$,
$F_{3}=k\displaystyle \frac{Q(-3q)}{(2\mathrm{d})^{2}}=-\frac{3}{4}F$,
$F_{4}=k\displaystyle \frac{Q(-4q)}{(3\mathrm{d})^{2}}=-\frac{4}{9}F$, and
$F_{5}=k\displaystyle \frac{Q(-5q)}{(2\mathrm{d})^{2}}=-\frac{5}{4}F$.
Ranking the magnitudes
$\mathrm{F}_{1} \lt F_{2} \lt F_{4} \lt F_{3} \lt F_{5}$.
