Xiaosheng Huang, David Alvarez-Garcia, Monica Ubeda, Vikram Bhamre, Sean Xu, S. Baltasar, N. Ratier-Werbin, F. Urcelay, S. Agarwal, A. Cikota, Y. Hsu, E. Lin, D. J. Schlegel, E. Silver, C. J. Storfer, M. Tamargo-Arizmend

We present six galaxy-scale strong lenses with HST imaging modeled using GIGA-Lens. This is Paper V of the DESI Strong Lens Foundry series. These systems were discovered in the DESI Legacy Imaging Surveys using ML/AI methods and confirmed with DESI, Keck/NIRES, and VLT/MUSE spectroscopy. They span $z_d = 0.39 - 1.1$ and $z_s = 1.4 - 3.3$. This is the first HST strong lens sample modeled with full forward modeling -- all lens and source parameters sampled simultaneously in a single inference -- with explicit convergence validation using both $\widehat{R}$ and effective sample size (ESS) for each system. All inferred parameters satisfy $\widehat{R} < 1.1$ and ${\rm ESS} \gtrsim 10,000$, demonstrating that GIGA-Lens achieves statistically robust inference even for some of the most complex galaxy-scale lenses known. These results pave the way for scaling to much larger, high-resolution strong lens samples from HST, Euclid, JWST, and Roman. Convergence-validated modeling will be critical for key science goals, including constraining the mass-density profile of galaxies, detecting low-mass dark matter (sub)halos, and delivering precise and accurate cosmological constraints.