Single crystals with the composition Sr5Ir3O11 were found to grow in the system SrO-IrO2. A single-crystal structure determination [tetragonal, space group I4/mmm, with a = 3.890(1) and c = 16.890(10) angstrom, and R = 0.050] revealed alternate stacking of single and double IrO6 perovskite layers interleaved with SrO layers along the c-axis. Although the refined metal-oxygen distances were quite reasonable, the thermal parameters of one "heavy" atom (iridium) and one "light" atom (oxygen) were non-positive definite. Careful examination of Weissenberg and transmission electron microscopy photographs showed that the single crystals actually contained random distributions of single and double IrO6 perovskite layers arising from the intergrowth of Sr2IrO4 and Sr3Ir2O7 phases. This paper serves as a cautionary tale for those who rely solely on diffractometer data for their structural analyses.