  The RG functions of the 2D $n$-vector $\phi^4$ model are calculated in the
five-loop approximation. Perturbative series for the $\beta$ function and
critical exponents are resummed by the Pade-Borel and Pade-Borel-Leroy
techniques, resummation procedures are optimized and an accuracy of the
numerical results is estimated. In the Ising case $n = 1$ as well as in the
others ($n = 0$, $n = -1$, $n = 2, 3,...32$) an account for the five-loop term
is found to shift the Wilson fixed point location only briefly, leaving it
outside the segment formed by the results of the corresponding lattice
calculations; even error bars of the RG and lattice estimates do not overlap in
the most cases studied. This is argued to reflect the influence of the singular
(non-analytical) contribution to the $\beta$ function that can not be found
perturbatively. The evaluation of the critical exponents for $n = 1$, $n = 0$
and $n = -1$ in the five-loop approximation and comparison of the numbers
obtained with their known exact counterparts confirm the conclusion that
non-analytical contributions are visible in two dimensions.
