  A new approach to summation of divergent field-theoretical series is
suggested. It is based on the Borel transformation combined with a conformal
mapping and does not imply the exact asymptotic parameters to be known. The
method is tested on functions expanded in their asymptotic power series. It is
applied to estimating the critical exponent values for an N-vector field model,
describing magnetic and structural phase transitions in cubic and tetragonal
crystals, from five-loop \epsilon expansions.
