Answer
$v = 21ms^{-1}$
Work Step by Step
Momentum of photon is given by
$$p_{photon} = {h\over \lambda}$$
For $N$ photons,
$$p_{Nphotons} = {Nh\over \lambda}$$
As glow worm is ejecting photons and no external force is acting on it.
$\therefore $ Linear momentum is conserved.
Hence, $\frac{Nh}{\lambda} = p_{glowworm}$
$\frac{Nh}{\lambda} = mv$, $\qquad ......(i)$
where $m$ is mass of glowworm and $v$ is the velocity attained by glowworm.
Glowworm is ejecting photons at a power of 0.10W
$P = \frac{E}{t} = \frac{Nhc}{\lambda t}$
$\frac{Nh}{\lambda} = {Pt\over c}$
Hence, equation $(i)$ becomes,
$mv = {Pt\over c}$
$v = {Pt\over mc}$
Given $P = 0.10W$, $t = 10 years = 10\times 365\times 86400 sec$
$m = 5g = 5\times 10^{-3}kg,c = 3\times 10^8$
$\therefore v = {\frac{0.1\times 10\times 365\times 86400}{5\times 10^{-3}\times 3\times 10^8}}m/s = 21m/s$
