Aims: The knowledge of physical conditions in young radio sources is important for defining the framework of models describing radio source evolution. We investigate whether young radio sources are in equipartition (i.e. minimum energy) conditions by comparing the equipartition magnetic fields of 5 High Frequency Peakers (HFP) with values directly inferred from the spectral peak assumed to be produced by synchrotron self absorption. Methods: Multi-frequency VLBA observations of 5 HFPs were carried out in both the optically thick and thin part of the spectrum to determine the spectral shape and angular size of the components for which individual radio spectra were obtained. Results: We find that the magnetic fields measured using observations agree well with those obtained by assuming equipartition, which implies that these sources are in minimum energy condition and the turnover in their spectra is due probably to SSA. In two source components, we found that the peak of the spectrum is caused by absorption of a thermal plasma instead of being due to SSA. The magnetic fields found in the various components range from 10 to 100 mG. In the presence of such high magnetic fields, electron populations with rather low γ emit in the GHz-regime. In one source, we detect low-surface brightness extended emission at low frequency located ~30 mas (~50 pc) from the main source. This feature may be related to either an earlier episode of radio activity or a discontinuous start of the radio activity (sputtering). By comparing our data with previous VLBA observations, we estimate the hotspot advance speed to be in the range 0.1-0.7c and kinematic ages of a few hundred years.