  We present the first demonstration of multi-GeV laser wakefield acceleration
in a fully optically formed plasma waveguide, with an acceleration gradient as
high as 25 GeV/m. The guide was formed via self-waveguiding of <15 J, 45 fs
(<~300 TW) pulses over 20 cm in a low density hydrogen gas jet, with
accelerated electron bunches simultaneously driven up to 5 GeV in a milliradian
divergence quasi-monoenergetic peak of relative energy width ~15% and charge of
at least ~10 picocoulombs. Energy gain is inversely correlated with on-axis
waveguide density in the range N_e0=(1.3-3.2)x10^17 cm^(-3). We find that
shot-to-shot stability of bunch spectra and charge are strongly dependent on
the pointing of the injected laser pulse and gas jet uniformity. We also
observe evidence of pump depletion-induced dephasing, a consequence of the long
optical guiding distance.
