We have constructed a specialized experimental setup with integrated magnetic field independent thermometry, which has enabled us to cool the charge carriers in two dimensional electron gases down to 5 mK, and reliably measure the temperature. Using this setup, we have conducted studies of ν=5/2 fractional quantum Hall state(FQHS) in so far unexplored regions of the parameter space. Using a sample with a tunable density, we observe, for the first time, an evidence of a transition at ν=5/2 filling factor. This transition takes place at the lowest density at which ν=5/2 state had been measured to date, around 6x1010cm-2. Using a different set of samples, we also demonstrate a consistent way to account for the disorder contribution to the energy gap of ν=5/2 FQHS for several samples of vastly different densities. This lets us quantify, for the first time, the dependence of the experimentally measured intrinsic gap at ν=5/2 on Landau level mixing alone. Finally, we have conducted an ultra-low temperature study of the fractional quantum Hall states in the 1/3\u3cν\u3c2/5 region. Due to the residual interaction of composite fermions, this region is thought to support next generation FQHS. Similarly to an earlier report, at the relatively high temperature of 51mK, the magnetoresistance exhibits developing FQHS at ν=4/11; 5/13, 6/17 and 3/8. However, we find that at lower temperatures only the ν=4/11 and 5/13 develop incompressibility, while the ν=6/17 and 3/8 remain compressible