We present a study of the inclusive charged-particle transverse momentum (p_T) spectra as a function of charged-particle multiplicity density at mid-pseudorapidity, d N_ch/ d η, in pp collisions at s=5.02 and 13 TeV covering the kinematic range | η| < 0.8 and 0.15 < p_T< 20 GeV/c. The results are presented for events with at least one charged particle in | η| < 1 (INEL>0). The p_T spectra are reported for two multiplicity estimators covering different pseudorapidity regions. The p_T spectra normalized to that for INEL>0 show little energy dependence. Moreover, the high-p_T yields of charged particles increase faster than the charged-particle multiplicity density. The average p_T as a function of multiplicity and transverse spherocity is reported for pp collisions at s=13 TeV. For low- (high-) spherocity events, corresponding to jet-like (isotropic) events, the average p_T is higher (smaller) than that measured in INEL>0 pp collisions. Within uncertainties, the functional form of ⟨ p_T⟩ (N_ch) is not affected by the spherocity selection. While EPOS LHC gives a good description of many features of data, PYTHIA overestimates the average p_T in jet-like events.