Let us determine the dimensional formula of each physical quantity involved: Energy ($E$) = $[M L^2 T^{-2}]$ Mass ($m$) = $[M]$ Angular momentum ($l$) = $[M L^2 T^{-1}]$ Gravitational constant ($G$) = $[M^{-1} L^3 T^{-2}]$

Substituting these dimensions into the given expression $\frac{E l^2}{m^5 G^2}$: $\frac{[M L^2 T^{-2}] \times [M L^2 T^{-1}]^2}{[M]^5 \times [M^{-1} L^3 T^{-2}]^2} = \frac{[M L^2 T^{-2}] \times [M^2 L^4 T^{-2}]}{[M^5] \times [M^{-2} L^6 T^{-4}]}$ $= \frac{[M^3 L^6 T^{-4}]}{[M^3 L^6 T^{-4}]} = [M^0 L^0 T^0]$

The resulting dimension is $[M^0 L^0 T^0]$, which indicates a dimensionless quantity. Among the given options, Angle is defined as the ratio of arc length to radius ($[L]/[L]$) and is a dimensionless quantity.