Five isomers of the carbon-rich molecule C5H2 are investigated computationally, using methods based on the coupled-cluster approximation. All of these structures are related to isomers of C3H2 via substitution of hydrogen by ethynyl or attachment of a C-2 fragment to a carbene center. The two most stable forms of C5H2 are linear triplet pentadiynylidene (4) and singlet ethynylcyclopropenylidene (6). Both of these isomers have been observed in the laboratory, as has a third-the cumulene carbene pentatetraenylidene (5)-which is predicted to lie about 15 kcal/ mol above the linear triplet. Two other isomers are also studied: ethynylpropadienylidene (7) and 3-(didehydro-vinylidene)cyclopropene (8). Both are found to lie less than 25 kcal/mol above the most stable form of C5H2 and to possess rather large dipole moments. Predictions for the harmonic vibrational frequencies of C-12 and mono-C-13 isotopomers, infrared intensities, and rotational constants are also presented. These should assist efforts to identify these molecules in the laboratory and in the interstellar medium.