The 5 subunit core of TFIIH that has tightly associated subunits and is found in both the general transcription factor holo-TFIIH and in the nucleotide-excision repair factor 3 complex. In S. cerevisiae, it is composed of Rad3, Tfb1, Tfb2, Ssl1, Tfb4. In humans, it is composed of XPD, p62, p55, p44, p34.