  In this work we report deep MUSE observations of a Broad Absorption Line
(BAL) quasar at z ~ 5, revealing a Lyman alpha nebula with a maximum projected
linear size of ~ 60 kpc around the quasar (down to our 2-sigma SB limit per
layer of ~ 9e-19 erg/s/cm^2/arcsec^2 for a 1 arcsec^2 aperture). After
correcting for the cosmological surface brightness dimming, we find that our
nebula, at z ~ 5, has an intrinsically less extended Lyman alpha emission than
nebulae at lower redshift. However, such a discrepancy is greatly reduced when
referring to comoving distances, which take into account the cosmological
growth of dark matter (DM) haloes, suggesting a positive correlation between
the size of Lyman alpha nebulae and the sizes of DM haloes/structures around
quasars. Differently from the typical nebulae around radio-quiet non-BAL
quasars, in the inner regions (~ 10 kpc) of the circumgalactic medium (CGM) of
our source, the velocity dispersion of the Lyman alpha emission is very high
(FWHM > 1000 km/s), suggesting that in our case we may be probing outflowing
material associated with the quasar.
