We report the discovery of two unsaturated organic species, trans-(E)-cyanovinylacetylene and vinylcyanoacetylene, using the second data release of the GOTHAM deep survey toward 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 (∼3σ). From this analysis, we derive column densities of 2 × 1011 and 3 × 1011 cm-2 for vinylcyanoacetylene and trans-(E)-cyanovinylacetylene, respectively, and an upper limit of for vinylcyanoacetylene and trans-(E)-cyanovinylacetylene, respectively, and an upper limit of 11 cm-2 for trans-(Z)-cyanovinylacetylene. Comparisons with G3//B3LYP semiempirical thermochemical calculations indicate abundances of the [H3C5N] isomers are not consistent with their thermodynamic stability, and instead their abundances are mainly driven by dynamics. We provide a discussion on how these species may be formed in TMC-1, with reference to related molecules like vinyl cyanide (CH2 = CHC ≡ N). As part of this discussion, we performed the same analysis for ethyl cyanide (CH3CH2C ≡ N), the hydrogenation product of CH2 = CHC ≡ N. This analysis provides evidence-at 4.2σ significance-of an upper limit to the column density of = CHC ≡ N. This analysis provides evidence-at 4.2σ significance-of an upper limit to the column density of 11 cm-2; an order of magnitude lower than previous upper limits toward this source.