We demonstrate nonlinear pulse compression based on recently introduced highly coherent broadband supercontinuum (SC) generation in all-normal dispersion photonic crystal fiber (ANDi PCF). The special temporal properties of the octave-spanning SC spectra generated with 15 fs, 1.7 nJ pulses from a Ti:Sapphire oscillator in a 1.7 mm fiber piece allow the compression to 5.0 fs high quality pulses by linear chirp compensation with a compact chirped mirror compressor. This is the shortest pulse duration achieved to date from the external recompression of SC pulses generated in PCF. Numerical simulations in excellent agreement with the experimental results are used to discuss the scalability of the concept to the single-cycle regime employing active phase shaping. We show that previously reported limits to few-cycle pulse generation from compression of SC spectra generated in conventional PCFs possessing one or more zero dispersion wavelengths do not apply for ANDi PCF.