  We prove the existence of a global solution of the energy-critical focusing
wave equation in dimension $5$ blowing up in infinite time at any $K$ given
points $z_k$ of $\mathbb{R}^5$, where $K\geq 2$. The concentration rate of each
bubble is asymptotic to $c_k t^{-2}$ as $t\to \infty$, where the $c_k$ are
positive constants depending on the distances between the blow-up points $z_k$.
This result complements previous constructions of blow-up solutions and
multi-solitons of the energy-critical wave equation in various dimensions
$N\geq 3$.
