  We present new $AdS_5$ solutions in 11d supergravity and identify them as the
gravity duals of a class of 4d $\mathcal N = 2$ SCFTs of Argyres-Douglas type,
engineered by a stack of M5-branes wrapped on a sphere with one irregular
puncture and one regular puncture. The gravity solutions feature an internal
M5-brane source, which is dual to the irregular puncture. Thanks to a novel
St\"uckelberg mechanism involving an axion originating from the expansion of
the M-theory 3-form, one of the isometry generators on the gravity side is not
mapped to a continuous symmetry on the SCFT side.
