In this study we examine the radial dependence of the inertial and dissipation range indices, as well as the spectral break separating the inertial and dissipation range in power density spectra of interplanetary magnetic field fluctuations using Parker Solar Probe data from the fifth solar encounter between ∼0.1 and ∼0.7 au. The derived break wavenumber compares reasonably well with previous estimates at larger radial distances and is consistent with gyro-resonant damping of Alfvénic fluctuations by thermal protons. We find that the inertial scale power-law index varies between approximately −1.65 and −1.45. This is consistent with either the Kolmogorov (−5/3) or Iroshnikov–Kraichnan (−3/2) values, and has a very weak radial dependence with a possible hint that the spectrum becomes steeper closer to the Sun. The dissipation range power-law index, however, has a clear dependence on radial distance (and turbulence age), decreasing from −3 near 0.7 au (4 days) to −4 [±0.3] at 0.1 au (0.75 days) closer to the Sun.