We have studied the rotational mobility of a mixt. of butane and pentane on zeolite ZK-5 as a function of temp. from 1H-13C cross-relaxation at 4.7 and 11.7 T. In the studied temp. range (130-320 K), the sorbed alkanes are practically confined inside the a and g cages of ZK-5. This is confirmed by well-resolved peaks in magic-angle-spinning (MAS) 13C NMR spectra for each alkane in each cage. Despite the translational confinement, the obsd. NMR relaxation for the methylene groups of butane and pentane reflects extensive rotational motion inside cages. The max. cross-relaxation rates indicate a combination of ultrafast rotation about the alkane axis (including internal bond rotations) and a slower tumbling of the mol. axis itself. Two temp. regimes can be distinguished. Above 200 K, the effective tumbling times derived from the initial cross-relaxation show Arrhenius behavior with activation energies between 5 and 15 kJ/mol. Below 200 K, the motion becomes less activated. We consider various possible explanations and discuss three models: (A) a combination of activated and nonactivated motion, (B) a Gaussian distribution of activation energies, (C) concerted sorbate-zeolite motions. Model C involves a flexible zeolite lattice, which accommodates the binding of mols. by small dynamic deformations.