  A search for long-lived particles (LLPs) using 140 fb$^{-1}$ of $pp$
collision data with $\sqrt{s} = 13$ TeV recorded by the ATLAS experiment at the
LHC is presented. The search targets LLPs with masses between $5$ and $55$ GeV
that decay hadronically in the ATLAS inner detector. Benchmark models with LLP
pair production from exotic decays of the Higgs boson and models featuring
long-lived axion-like particles (ALPs) are considered. No significant excess
above the expected background is observed. Upper limits are placed on the
branching ratio of the Higgs boson to pairs of LLPs, the cross-section for ALPs
produced in association with a vector boson, and, for the first time, on the
branching ratio of the top quark to an ALP and a $u/c$ quark.
