  We describe intersecting M5-branes, as well as M5-branes wrapping the
holomorphic curve xy=c, in terms of a limit of a defect conformal field theory
with two-dimensional (4,0) supersymmetry. This dCFT describes the low-energy
theory of intersecting D3-branes at a C^2/Z_k orbifold. In an appropriate k ->
infinity limit, two compact spatial directions are generated. By identifying
moduli of the M5-M5 intersection in terms of those of the dCFT, we argue that
the SU(2)_L R-symmetry of the (4,0) defect CFT matches the SU(2) R-symmetry of
the N =2, d=4 theory of the M5-M5 intersection. We find a 't Hooft anomaly in
the SU(2)_L R-symmetry, suggesting that tensionless strings give rise to an
anomaly in the SU(2) R-symmetry of intersecting M5-branes.
