  Among efforts to detect gravitational radiation, pulsar timing arrays are
uniquely poised to detect "memory" signatures, permanent perturbations in
spacetime from highly energetic astrophysical events such as mergers of
supermassive black hole binaries. The North American Nanohertz Observatory for
Gravitational Waves (NANOGrav) observes dozens of the most stable millisecond
pulsars using the Arecibo and Green Bank radio telescopes in an effort to
study, among other things, gravitational wave memory. We herein present the
results of a search for gravitational wave bursts with memory (BWMs) using the
first five years of NANOGrav observations. We develop original methods for
dramatically speeding up searches for BWM signals. In the directions of the sky
where our sensitivity to BWMs is best, we would detect mergers of binaries with
reduced masses of $10^9$ $M_\odot$ out to distances of 30 Mpc; such massive
mergers in the Virgo cluster would be marginally detectable. We find no
evidence for BWMs. However, with our non-detection, we set upper limits on the
rate at which BWMs of various amplitudes could have occurred during the time
spanned by our data--e.g., BWMs with amplitudes greater than $10^{-13}$ must
occur at a rate less than 1.5 yr$^{-1}$.
