  The photoproduction reaction of $\gamma p \to K^+\Lambda(1405)$ is
investigated based on an effective Lagrangian approach at the tree-level
approximation with the purpose of understanding the reaction mechanism and
extracting the resonance contents and the associated resonance parameters in
this reaction. Apart from the $t$-channel $K$ and $K^\ast$ exchanges,
$s$-channel nucleon ($N$) exchange, $u$-channel $\Sigma$, $\Lambda$, and
$\Lambda(1405)$ exchanges, and generalized contact term, the exchanges of a
minimum number of $N$ resonances in the $s$ channel are taken into account in
constructing the reaction amplitudes to describe the experimental data. It is
found that by introducing the $N(2000){5/2}^+$ resonance exchange in the $s$
channel, one can reproduce the most recent differential cross-section data from
the CLAS Collaboration quite well. Further analysis shows that the cross
sections of $\gamma p \to K^+\Lambda(1405)$ at high energies are dominated by
the $t$-channel $K$ exchange, while the contributions from the $s$-channel $N$
and $N(2000){5/2}^+$ exchanges are rather significant to the cross sections in
the near-threshold energy region. Predictions for the beam and target
asymmetries for $\gamma p \to K^+\Lambda(1405)$ are given.
