Tubulin-folding protein; involved in the final step of the tubulin folding pathway. Supercomplex made of cofactors A to E. Cofactors A and D function by capturing and stabilizing tubulin in a quasi-native conformation. Cofactor E binds to the cofactor D-tubulin complex; interaction with cofactor C then causes the release of tubulin polypeptides that are committed to the native state (By similarity). Detected predominantly in the photoreceptor connecting cilium. Belongs to the TBCC family.