Answer
$ 16.3\;\rm kJ$
Work Step by Step
We have here 5 stages of heating:
1) Heating the ice from -20$^\circ$C to 0$^\circ$C, and the heat needed for that is given by
$$Q_1=mc_{ice}\Delta T_{ice}$$
2) Melting the ice at 0$^\circ$C until all of it became water, and the heat needed for that is given by
$$Q_2=mL_{{\rm f},ice} $$
3) Heating the water from 0$^\circ$C to 100$^\circ$C, and the heat needed for that is given by
$$Q_3=mc_{water}\Delta T_{water}$$
4) Evaporating the water at 100$^\circ$C until all the water became steam, and the heat needed for that is given by
$$Q_4=mL_{{\rm v},water} $$
5) Heating the steam from 100$^\circ$C to 200$^\circ$C, and the heat needed for that is given by
$$Q_5=mc_{steam}\Delta T_{steam}$$
Thus, the total heat needed is given by
$$Q=Q_1+Q_2+Q_3+Q_4+Q_5$$
$$Q=mc_{ice}\Delta T_{ice}+mL_{{\rm f},ice} +mc_{water}\Delta \\T_{water}+mL_{{\rm v},water}+mc_{steam}\Delta T_{steam}$$
$$Q=m\left[c_{ice}\Delta T_{ice}+ L_{{\rm f},ice} + c_{water}\Delta T_{water}+ L_{{\rm v},water}+ c_{steam}\Delta T_{steam}\right]$$
Plugging the known;
$$Q=(5\times 10^{-3})\left[(2090)(20)+ (3.33\times 10^5) + (4190)(100)+ (22.6\times 10^5)+ (2017)(100)\right]$$
$$Q=\color{red}{\bf 1.63\times 10^4}\;\rm J$$