The oxidation number of phosphorus in ${\mathrm{Mg}}_2{\mathrm{P}}_2{\mathrm{O}}_7$ is:

Let x represent the P oxidation number in ${\mathrm{Mg}}_2{\mathrm{P}}_2{\mathrm{O}}_7$

Since the oxidation number of the Mg atoms is +2 and the oxidation number of the O atoms is 2.

$\begin{array}{l}2(+2)+2x+7(-2)=0\\ 2x-10=0\\ 2x=10\\ x=+5\end{array}$

Hence, the oxidation number of P in ${\mathrm{Mg}}_2{\mathrm{P}}_2{\mathrm{O}}_7\text{ is }+5$.

So, option C is correct.