  For the 5D energy-critical wave equation, we construct excited $N$-solitons
with collinear speeds, i.e. solutions $u$ of the equation such that
  \begin{equation*}
  \lim_{t\to+\infty}\bigg\|\nabla_{t,x}u(t)-\nabla_{t,x}\bigg(\sum_{n=1}^{N}Q_{n}(t)\bigg)\bigg\|_{L^{2}}=0,
  \end{equation*} where for $n=1,\ldots,N$, $Q_n(t,x)$ is the Lorentz transform
of a non-degenerate and sufficiently decaying excited state, each with
different but collinear speeds. The existence proof follows the ideas of
Martel-Merle and C\^ote-Martel developed for the energy-critical wave and
nonlinear Klein-Gordon equations. In particular, we rely on an energy method
and on a general coercivity property for the linearized operator.
