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.
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