The electron and nuclear spins of donor impurities in enriched $^{28}\mathrm{Si}$ have great potential as long-lived qubits for a silicon-based quantum information technology. The ability to resolve the hyperfine-split neutral donor ground-state levels in the near-infrared donor bound exciton transitions of the ubiquitous phosphorus impurity in highly isotopically enriched $^{28}\mathrm{Si}$ has led to new methods of hyperpolarizing and measuring the donor electron and nuclear spins. This has resulted in optically assisted magnetic resonance methods that have permitted the measurement of remarkably long nuclear coherence times for both the neutral and ionized phosphorus donor in very lightly doped and highly enriched $^{28}\mathrm{Si}$. Other shallow donors such as arsenic, antimony, and bismuth offer the potential of larger hyperfine couplings and nuclear spins as compared to phosphorus. Here, we investigate whether donor bound exciton transitions can be used to initialize and read out the nuclear spins of arsenic and antimony in $^{28}\mathrm{Si}$. The projective readout of the electron and nuclear spins is demonstrated for both $^{75}\mathrm{As}$ and $^{121}\mathrm{Sb}$, and these optical transitions can strongly hyperpolarize the nuclear spin of $^{75}\mathrm{As}$. Only a small nuclear hyperpolarization is achieved for $^{121}\mathrm{Sb}$, likely due to the relative weakness of the no-phonon transition of the Sb donor bound exciton. Optically assisted EPR and NMR is demonstrated for $^{75}\mathrm{As}$, including Hahn echo coherence time measurements of the six NMR transitions.