We present the first pulsar parallaxes measured with phase-referenced pulsar VLBI observations at 5 GHz. Due to the steep spectra of pulsars, previous astrometric measurements have been at lower frequencies. However, the strongest pulsars can be observed at 5 GHz, offering the benefit of lower combined ionospheric and tropospheric phase errors, which usually limit VLBI astrometric accuracy. The pulsars B0329+54, B0355+54 and B1929+10 were observed for 7 epochs spread evenly over 2 years. For B0329+54, large systematic errors lead to only an upper limit on the parallax (pi < 1.5 mas). A new proper motion and parallax were measured for B0355+54 (pi = 0.91 +- 0.16 mas), implying a distance of 1.04+0.21-0.16 kpc and a transverse velocity of 61+12-9 km/s. The parallax and proper motion for B1929+10 were significantly improved (pi = 2.77 +- 0.07 mas), yielding a distance of 361+10-8 pc and a transverse velocity of 177+4-5 km/s. We demonstrate that the astrometric errors are correlated with the angular separation between the phase reference calibrator and the target source, with significantly lower errors at 5 GHz compared to 1.6 GHz. Finally, based on our new distance determinations for B1929+10 and B0355+54, we derive or constrain the luminosities of each pulsar at high energies. We show that, for thermal emission models, the emitting area for X-rays from PSR B1929+10 is roughly consistent with the canonical size for a heated polar cap, and that the conversion of spin-down power to gamma-ray luminosity in B0355+54 must be low. The new proper motion for B1929+10 also implies that its progenitor is unlikely to have been the binary companion of the runaway O-star zeta-Ophiuchi.
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