E, m, l and G denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of El²/m⁵G² are

The correct option is Angle.

To determine the dimensions of the given expression, we can find the dimensional formula of each individual physical quantity involved.

Let mass, length, and time be represented by $M$, $L$, and $T$ respectively.

1. Energy ($E$):
Energy has the same dimensions as work done (force × displacement).
$\left[E\right]=\left[\text{Force}\right]\times \left[\text{Displacement}\right]=\left({\mathrm{MLT}}^{-2}\right)\times L={\mathrm{ML}}^2{T}^{-2}$

2. Angular Momentum ($l$):
Angular momentum is given by the product of mass, velocity, and distance ($l=mvr$).
$\left[l\right]=M\times \left({\mathrm{LT}}^{-1}\right)\times L={\mathrm{ML}}^2{T}^{-1}$
Thus, the dimension of $l^2$ is:
$\left[l^2\right]=M^2{L}^4{T}^{-2}$

3. Mass ($m$):
The dimension of mass is:
$\left[m\right]=M$
Thus, the dimension of $m^5$ is:
$\left[m^5\right]=M^5$

4. Universal Gravitational Constant ($G$):
From Newton's law of gravitation, we have $F=\frac{G{m}^2}{r^2}$, which gives:
$G=\frac{F{r}^2}{m^2}$
$\left[G\right]=\frac{\left({\mathrm{MLT}}^{-2}\right)\times L^2}{M^2}=M^{-1}{L}^3{T}^{-2}$
Thus, the dimension of $G^2$ is:
$\left[G^2\right]=M^{-2}{L}^6{T}^{-4}$

Now, let us substitute these dimensional formulas into the expression $\frac{E{l}^2}{m^5{G}^2}$:

$\left[\frac{E{l}^2}{m^5{G}^2}\right]=\frac{\left({\mathrm{ML}}^2{T}^{-2}\right)\times \left(M^2{L}^4{T}^{-2}\right)}{M^5\times \left(M^{-2}{L}^6{T}^{-4}\right)}$

Simplifying the numerator:
$\left[\text{Numerator}\right]=M^{1+2}{L}^{2+4}{T}^{-2-2}=M^3{L}^6{T}^{-4}$

Simplifying the denominator:
$\left[\text{Denominator}\right]=M^{5-2}{L}^6{T}^{-4}=M^3{L}^6{T}^{-4}$

Dividing the numerator by the denominator:
$\left[\frac{E{l}^2}{m^5{G}^2}\right]=\frac{M^3{L}^6{T}^{-4}}{M^3{L}^6{T}^{-4}}=M^0{L}^0{T}^0$

Since the resulting dimension is $M^0{L}^0{T}^0$, the expression is dimensionless. Among the given options, an Angle is a dimensionless quantity (defined as arc length divided by radius, which is $L/L=L^0$).