Given: $X = 5YZ^{2}$,

$X$ has Dimensional formula of capacitance $\left( C = \frac{\varepsilon_{0}\text{\ }A}{d} \right)$

$\lbrack X\rbrack = \left\lbrack M^{- 1}{\text{\ }L}^{- 2}{\text{\ }T}^{4}{\text{\ }A}^{2} \right\rbrack\text{.~}$

$Z$ has dimensional formula of magnetic field $\left( B = \frac{F}{I^{l}} \right)$

$\lbrack Z\rbrack = \left\lbrack M^{- 1}{\text{\ }T}^{- 2}{\text{\ }A}^{- 1} \right\rbrack\text{.~}$

To find: Dimensions of $Y \propto \frac{X}{5Z^{2}}.$

Putting dimensions of $X$ and $Y$ from (i) and (ii) in equation (iii),

$\lbrack Y\rbrack = \left\lbrack M^{- 1}{\text{\ }L}^{- 2}{\text{\ }T}^{4}{\text{\ }A}^{2} \right\rbrack\left\lbrack M^{1}{\text{\ }T}^{- 2}{\text{\ }A}^{- 1} \right\rbrack^{- 2}$

$\lbrack Y\rbrack = M^{- 3}{\text{\ }L}^{- 2}{\text{\ }T}^{8}{\text{\ }A}^{4}$