  It was proved in [8,9] that every Lagrangian submanifold $M$ of a complex
space form $\tilde M^{5}(4c)$ of constant holomorphic sectional curvature $4c$
satisfies the following optimal inequality: {align}\tag{A}\delta(2,2)\leq
\text{\small${25}{4}$} H^{2}+8c,{align} where $H^{2}$ is the squared mean
curvature and $\delta(2,2)$ is a $\delta$-invariant on $M$ introduced by the
first author. This optimal inequality improves a special case of an earlier
inequality obtained in [B.-Y. Chen, Japan. J. Math. 26 (2000), 105-127].
  The main purpose of this paper is to classify Lagrangian submanifolds of
$\tilde M^{5}(4c)$ satisfying the equality case of the improved inequality (A).
