A new system of units is proposed in which unit of mass is $\alpha$ kg, unit of length is $\beta$ m and unit of time is $\gamma$s. What will be value of 5J in this new system?

Joule is a unit of energy.

Dimensional formula of energy is $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$. Comparing with $\left[M^a{L}^b{T}^c\right]$, we get $a=1,b=2,c=-2$

As ${\mathrm{n}}_2={\mathrm{n}}_1{\left(\frac{{\mathrm{M}}_1}{{\mathrm{M}}_2}\right)}^{\mathrm{a}}{\left(\frac{{\mathrm{L}}_1}{{\mathrm{L}}_2}\right)}^{\mathrm{b}}{\left(\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}\right)}^{\mathrm{c}}$

$\text{=5}{\left(\frac{1\mathrm{kg}}{\alpha \mathrm{kg}}\right)}^{\mathrm{\prime }}{\left(\frac{1\mathrm{m}}{\beta \mathrm{m}}\right)}^2{\left(\frac{1\mathrm{s}}{\gamma \mathrm{s}}\right)}^{-2}=\frac{5{\gamma }^2}{\alpha {\beta }^2}=5{\alpha }^{-1}{\beta }^{-2}{\gamma }^2$