  We study probe M5-branes in N=1 AdS5 solutions of M-theory that arise from
M5-branes wrapped on a Riemann surface. Using the BPS condition from
kappa-symmetry, we classify supersymmetric probe M5-branes that extend along
all of AdS5 and intersect the Riemann surface at points. These can be viewed as
punctures in the dual N=1 superconformal field theories. We find M5-branes that
correspond to the two types of simple punctures previously studied in field
theory. In addition, when the central charge is rational, we find a new class
of M5-branes with a moduli space that includes two internal dimensions in
addition to the Riemann surface. These new M5-branes have the essential
characteristic of fractional branes, in that a single one at a generic point of
its moduli space becomes multiple M5-branes at special points.
