...and this translates to nearly a factor of 5 increase of the output impedance of M3 and M4, which essentially determines the gain.
Now Rd = 1/(gm(M3)+gm(M5)) , and
gain ≈ gm(M1)/(gm(M3)+gm(M5))
M5 & M6 - with the same Vds as M3 & M4 - however can be operated with an (absolute) lower |Vb| than |Vgs=Vds|, hence will have a considerably lower gm, respectively higher Rd.
In practice - depending on the selected aspect ratio between M5/M3 (M6/M4) and the chosen inversion mode - one probably can't expect this full factor of five in gain enhancement.