Not the specific compounds $\ce{IH3}$ and $\ce{IH5}$, but hydrogen-iodine compounds with nonclassical stoichiometriws have been synthesized under high pressure.
Binns et al[1] report two high-pressure, hydrogen-rich hydrogen iodides. The more widely stable one, with empirical formula $\ce{H_{27}I}$ consisting of a hydrogen iodide molecule isolated in a shell of thirteen dihydrogen molecules, is stable from 9 to at least 130 GPa pressure. The second compound, stable up to 12.5 GPa, has two hydrogen iodide molecules per one dihydrogen molecules for an empirical formula $\ce{H2I}$. Both compounds are characterized by synchrotron XRD and Raman spectroscopy, and both have only secondary bonding between the hydrogen iodide component and additional hydrogen rather than hypercoordinated iodine.
Reference
- Jack Binns, Philip Dalladay-Simpson, Mengnan Wang, Graeme J. Ackland, Eugene Gregoryanz, and Ross T. Howie (2018)."Formation of H2-rich iodine-hydrogen compounds at high pressure".
Phys. Rev. B 97, 024111. https://doi.org/10.1103/PhysRevB.97.024111