  In this paper, we give a complete set of finite type string link invariants
of degree <5. In addition to Milnor invariants, these include several string
link invariants constructed by evaluating knot invariants on certain closure of
(cabled) string links. We show that finite type invariants classify string
links up to C_k-moves for k<6, which proves, at low degree, a conjecture due to
Goussarov and Habiro. We also give a similar characterization of finite type
concordance invariants of degree <6.
