  We report the discovery of two unsaturated organic species,
trans-(E)-cyanovinylacetylene and vinylcyanoacetylene, using the second data
release of the GOTHAM deep survey towards TMC-1 with the 100 m Green Bank
Telescope. For both detections, we performed velocity stacking and matched
filter analyses using Markov chain Monte Carlo simulations, and for
trans-(E)-cyanovinylacetylene, three rotational lines were observed at low
signal-to-noise (${\sim}$3$\sigma$). From this analysis, we derive column
densities of $2\times10^{11}$ and $3\times10^{11}$ cm$^{-2}$ for
vinylcyanoacetylene and trans-(E)-cyanovinylacetylene, respectively, and an
upper limit of $<2\times10^{11}$ cm$^{-2}$ for trans-(Z)-cyanovinylacetylene.
Comparisons with G3//B3LYP semi-empirical thermochemical calculations indicate
abundances of the [H$_3$C$_5$N}] isomers are not consistent with their
thermodynamic stability, and instead their abundances are mainly driven by
dynamics. We provide discussion into how these species may be formed in TMC-1,
with reference to related species like vinyl cyanide (CH$_2$=CHCN). As part of
this discussion, we performed the same analysis for ethyl cyanide
(CH$_3$CH$_2$CN), the hydrogenation product of CH$_2$=CHCN. This analysis
provides evidence -- at 4.17$\sigma$ significance -- an upper limit to the
column density of $<4\times10^{11}$ cm$^{-2}$; an order of magnitude lower than
previous upper limits towards this source.
