  Nevanlinna's five-value theorem is well-known as a famous theorem in value
distribution theory, which asserts that two non-constant meromorphic functions
on $\mathbb C$ are identical if they share five distinct values ignoring
multiplicities in $\overline{\mathbb C}.$ The central goal of this paper is to
generalize Nevanlinna's five-value theorem to non-compact complete K\"ahler
manifolds with non-positive sectional curvature by means of the theory of
algebraic dependence. With a certain growth condition imposed, we show that two
nonconstant meromorphic functions on such class of manifolds are identical if
they share five distinct values ignoring multiplicities in $\overline{\mathbb
C}.$
