SU(3) gauge theory with $N_f$ fermions in the fundamental representation serves as a theoretical testing ground for possible infrared conformal behavior, which could play a role in BSM composite Higgs models. We use lattice simulations to study the 10-flavor model, for which it has been claimed there is an infrared fixed point in the gauge coupling $beta$-function. Our results suggest the opposite conclusion, namely we find no $beta$-function fixed point in the explored range, with qualitative agreement with the 5-loop $overline{MS}$ prediction. We comment on the inconsistency between our findings and other studies.