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The existence of new previously unknown ternary aluminide with the composition very close to CeRhAl was established during the systematic investigation of the phase equilibria in the Ce-Rh-Al system. A single crystal of Ce5Rh5-xAl6+x suitable for data collection was isolated from the surface of the as-cast polycrystalline sample. The crystal structure was investigated at 298 K using a STOE STADI VARI PILATUS-100K diffractometer (w and j scans, MoKa radiation). The structure solution and refinement were done with the SHELX software package. All atoms were refined anisotropically. The cell setting was standardized with the STRUCTURE TIDY program. Ce5Rh5-xAl6+x crystallizes with own structure type: Pearson symbol oS64, space group Cmc21, a =4.251(2) Å, b =41.78(3) Å, c =7.141(4) Å, V = 1268.32(13) Å3. In accordance with the stoichiometry, the unit cell of the title compound contains five crystallographically independent Ce, five Rh, and six Al positions, wherein one of the Rh positions is partially occupied by Al atoms. The structure may be described as a two layers one formed by three different stripes of condensed pentagonal prisms divided by ½ a and shifted by ½ along the b-axis. The main feature of this structure is the shortest known cerium-rhodium distance of 2.609 Å. This work was performed within the RFBR projects 11-03-00957a and 11-03-01191a.