Rotational degrees of freedom (3N-5 and 3N-6)
Rotations around bonds are typically termed "internal rotations", and represent one of the most common problematic cases for the rigid-rotor-harmonic-oscillator (RRHO) model of internal molecular motion.  This is because RRHO assumes that any vibrational amplitudes are "small," and internal rotations are most definitely not small!  Such rotations still involve the internal degrees of freedom of the molecule, though, and thus (as Jan notes) are considered as part of the 'vibration' of the molecule, not its 'rotation.'

Internal rotations typically have some energy cost involved (as in your pentane example), and so cannot be treated as "free" rotations. They are usually termed "hindered rotations," and there is a great deal of literature studying them.  Some citations I know offhand:


Classic Pitzer (J Chem Phys 5 469, 1937), and Pitzer &amp; Gwinn (J Chem Phys 10 428, 1942)
Independent-rotations approximation for treating hindered internal rotation: Pfaendtner (Theor Chem Acc 118 881, 2007)
Other / more-advanced treatments of internal rotation:


Hecht (J Chem Phys 26 31, 1957)
Strekalov (Chem Phys 355 62, 2009)
Vansteenkiste (J Chem Phys 124 044314, 2006)
McClurg (J Chem Phys 106 6675, 1997)



One species of particular interest to me on this topic has been nitromethane, which has an extraordinarily small barrier to rotation around the $\ce{C}-\ce{N}$ bond (see Strekalov, above), such that at ambient temperature it can be considered essentially a free rotation.