By comparing photoemission spectroscopy with a non-perturbative dynamical mean field theory extension to many-body ab initio calculations, we show in the prominent case of pentacene crystals that an excellent agreement with experiment for the bandwidth, dispersion and lifetime of the hole carrier bands can be achieved in organic semiconductors provided that one properly accounts for the coupling to molecular vibrational modes and the presence of disorder. Our findings rationalize the growing experimental evidence that even the best band structure theories based on a many-body treatment of electronic interactions cannot reproduce the experimental photoemission data in this important class of materials.