  We report the first detection in space of the cumulene carbon chain
$l$-H$_2$C$_5$. A total of eleven rotational transitions, with $J_{up}$ = 7-10
and $K_a$ = 0 and 1, were detected in TMC-1 in the 31.0-50.4 GHz range using
the Yebes 40m radio telescope. We derive a column density of
(1.8$\pm$0.5)$\times$10$^{10}$ cm$^{-2}$. In addition, we report observations
of other cumulene carbenes detected previously in TMC-1, to compare their
abundances with the newly detected cumulene carbene chain. We find that
$l$-H$_2$C$_5$ is $\sim$4.0 times less abundant than the larger cumulene
carbene $l$-H$_2$C$_6$, while it is $\sim$300 and $\sim$500 times less abundant
than the shorter chains $l$-H$_2$C$_3$ and $l$-H$_2$C$_4$. We discuss the most
likely gas-phase chemical routes to these cumulenes in TMC-1 and stress that
chemical kinetics studies able to distinguish between different isomers are
needed to shed light on the chemistry of C$_n$H$_2$ isomers with $n$\,$>$\,3.
