  Basing on evaluation of the Racah coefficients for SU_q(3) (which supported
the earlier conjecture of their universal form) we derive explicit formulas for
all the 5-, 6- and 7-strand Wilson averages in the fundamental representation
of arbitrary SU(N) group (the HOMFLY polynomials). As an application, we list
the answers for all 5-strand knots with 9 crossings. In fact, the 7-strand
formulas are sufficient to reproduce all the HOMFLY polynomials from the
katlas.org: they are all described at once by a simple explicit formula with a
very transparent structure. Moreover, would the formulas for the relevant
SU_q(3) Racah coefficients remain true for all other quantum groups, the paper
provides a complete description of the fundamental HOMFLY polynomials for all
braids with any number of strands.
