  We report the discovery of the C5H+ cation toward TMC-1 with the QUIJOTE line
survey. Four lines from J=7-6 up to J=10-9 have been identified in perfect
harmonic frequency relation that can be fit with B=2411.94397 +/-0.00055 MHz
and D=138+/-3 Hz. The standard deviation of the fit is 4.4 kHz. After
discarding potential candidates, C5H- among them, we conclude that the carrier
is C5H+, for which accurate ab initio calculations provide B=2410.3 MHz. We
also report for the first time in a cold starless core the detection of the
C3H+ cation. The column densities we derive for C5H+ and C3H+ are
(8.8+/-0.5)e10 cm-2 and (2.4+/-0.2)e10 cm-2, respectively. Hence, the C5H+/C3H+
abundance ratio is 3.7+/-0.5. The fact that C5H+ is more abundant than C3H+ is
well explained by dedicated chemical models and is due to the slow reactivity
of C5H+ with H2, while C3H+ reacts with H2.
