Heterostructures composed of pentacene (PEN) molecules and transition metal dichalchogenides (TMDs) are promising materials for small, flexible and lightweight photovoltaic devices and various other optoelectronic applications. The effects of changing concentration and orientation of adsorbed PEN molecules on two-dimensional monolayer substrates of TMDs, namely MoS2, MoSe2, WS2 and WSe2, were investigated using first-principles calculations based on density functional theory. We examined the structural and electronic properties of the corresponding PEN/TMD heterostructures and compared these between differing PEN concentrations and the orientations of PEN with respect to the underlying substrate crystal structure. We analyze the band alignment of the heterostructures and demonstrate a concentration-dependent staggered-to-straddling (typeII-I) band gap transition in PEN/MoSe2.