  The renormalization group functions are calculated in $D=4-\epsilon$
dimensions for the $\phi^4$-theory with two coupling constants associated with
an ${O}(N)$-symmetric and a cubic interaction. Divergences are removed by
minimal subtraction. The critical exponents $\eta$, $\nu$, and $\omega$ are
expanded up to order $\epsilon^5$ for the three nontrivial fixed points
O(N)-symmetric, Ising, and cubic. The results suggest the stability of the
cubic fixed point for $N\geq3$, implying that the critical exponents seen in
the magnetic transition of three-dimensional cubic crystals are of the cubic
universality class. This is in contrast to earlier three-loop results which
gave $N > 3$, and thus Heisenberg exponents.
  The numerical differences, however, are less than a percent making an
experimental distinction of the universality classes very difficult.
