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