The flux of galactic cosmic rays (GCR) at Earth is modulated in the heliosphere by the heliospheric magnetic field and solar wind, that vary in the course of solar cycle. The modulation is caused by diffusion, convection, adiabatic cooling and drifts, where very important is scattering of particles on magnetic inhomogeneities in the turbulent solar wind and heliospheric magnetic field (HMF). Turbulent variations are often characterized by a power law in the power spectrum of the cosmic-ray variations. Previous works revealed a power law behaviour in the power spectral density (PSD) of GCR fluxes in the frequency range between $5.56\cdot 10^{-6}$ and $2.14\cdot 10^{-6}$ Hz (50 – 130 hours) that varies with the solar cycle phases. Here we further develop these results by employing a broader and higher-quality dataset obtained from the world data repository (the WDCCR). Using data from 31 ground-based neutron monitors (NMs) spanning 65 years (nearly six solar cycles, 1953—2018) of measurements, we have studied the spectral slopes of the PSD of NM count rates. Using 2-year overlapping PSD intervals, we found that the spectral slope varies in time between approximately -1 and -2.6, with a mean value of $1.84\pm 0.01$. Separating the results to specific solar cycle phases, we found that steep slopes close to -2.0 (typical for a random walk) appear during solar maximum times, and flatter slopes close to -1.7 (Kolmogorov-type spectrum) appear during solar cycle minimum times, indicating that different physical processes determine GCR transport in the Heliosphere at different phases of the solar cycle. We note that these results are in close agreement with the earlier results that used a different dataset.