  We consider circular non-BPS Maldacena-Wilson loops in five-dimensional
supersymmetric Yang-Mills theory (d = 5 SYM) both as macroscopic strings in the
D4-brane geometry and directly in gauge theory. We find that in the Dp-brane
geometries for increasing p, p = 4 is the last value for which the radius of
the string worldsheet describing the Wilson loop is independent of the UV
cut-off. It is also the last value for which the area of the worldsheet can be
(at least partially) regularized by the standard Legendre transformation. The
asymptotics of the string worldsheet allow the remaining divergence in the
regularized area to be determined, and it is found to be logarithmic in the UV
cut-off. We also consider the M2-brane in AdS_7 x S^4 which is the M-theory
lift of the Wilson loop, and dual to a "Wilson surface" in the (2,0), d = 6
CFT. We find that it has exactly the same logarithmic divergence in its
regularized action. The origin of the divergence has been previously understood
in terms of a conformal anomaly for surface observables in the CFT. Turning to
the gauge theory, a similar picture is found in d = 5 SYM. The divergence and
its coefficient can be recovered for general smooth loops by summing the
leading divergences in the analytic continuation of dimensional regularization
of planar rainbow/ladder diagrams. These diagrams are finite in 5 - epsilon
dimensions. The interpretation is that the Wilson loop is renormalized by a
factor containing this leading divergence of six-dimensional origin, and also
subleading divergences, and that the remaining part of the Wilson loop
expectation value is a finite, scheme-dependent quantity. We substantiate this
claim by showing that the interacting diagrams at one loop are finite in our
regularization scheme in d = 5 dimensions, but not for d greater than or equal
to 6.
