  In paper IV (solv-int/9704013) we have considered a string living in the
infinite lattice that was, in a sense, generated by a "particle". Here we show
how to construct multi-string eigenstates generated by several particles. It
turns out that, at least in some cases, this allows us to bypass the
difficulties of constructing multi-particle states. We also present and discuss
the "dispersion relations" for our particles-strings.
