How much should the pressure  be increased in order to decrease the volume of a gas by 5% at constant temperature 

We know that change in pressure is equal to the difference in the final pressure and the initial pressure. So, 5.26% of pressure must be increased in order to decrease the volume of the gas by 5%.

$\begin{array}{l}{\mathrm{P}}_1{ \mathrm{V}}_1={\mathrm{P}}_2{ \mathrm{V}}_2\\ { \mathrm{V}}_2=0.95{ \mathrm{V}}_1\left({\mathrm{AsV}}_2\text{ is }5\%\text{ less than }\left[{\mathrm{V}}_1\right]\right.\\ {\mathrm{P}}_1\times {\mathrm{V}}_1={\mathrm{P}}_2\times \left(\mathrm{O}.95{ \mathrm{V}}_1\right)\\ {\mathrm{P}}_1=\frac{{\mathrm{P}}_2\times \left({\mathrm{O}}_1.95{ \mathrm{V}}_1\right)}{{\mathrm{V}}_1}\\ {\mathrm{P}}_2=\frac{{\mathrm{P}}_1}{0.95}=1.052{\mathrm{P}}_1\end{array}$

$\%\text{ Increase in pressure }=\frac{\text{ final pressure }-\text{ initial pressure }}{\text{ Initial pressure }}\times 100$

$\text{ \% Increase in pressure }=\frac{1.052{\mathrm{P}}_1-{\mathrm{P}}_1}{{\mathrm{P}}_1}\times 100$

$=\frac{{\mathrm{P}}_1(1.052-1)}{{\mathrm{P}}_1}\times 100=0.052\times 100$

$\text{ Increase in pressure }=5.26\%$

hence, the correct option is option D.