In this paper, the problem of C2 Hermite interpolation by triarcs composed of Pythagorean-hodograph (PH) quintics is considered. The main idea is to join three arcs of PH quintics at two unknown points – the first curve interpolates given C2 Hermite data at one side, the third one interpolates the same type of given data at the other side and the middle arc is joined together with C2 continuity to the first and the third arc. For any set of C2 planar boundary data (two points with associated first and second derivatives) we construct four possible interpolants. The best possible approximation order is 4. Analogously, for a set of C2 spatial boundary data we find a six-dimensional family of interpolating quintic PH triarcs. The results are confirmed by several examples.