  The photoluminescence (PL) spectra of monolayer (1L) semiconductors feature
peaks ascribed to different charge-carrier complexes. We perform diffusion
quantum Monte Carlo simulations of the binding energies of these complexes and
examine their response to electric and magnetic fields. We focus on quintons
(charged biexcitons), since they are the largest free charge-carrier complexes
in transition-metal dichalcogenides (TMDs). We examine the accuracy of the
Rytova-Keldysh interaction potential between charges by comparing the binding
energies of charge-carrier complexes in 1L-TMDs with results obtained using
$\textit{ab initio}$ interaction potentials. Magnetic fields$<8$T change the
binding energies (BEs) by$\sim0.2$ meV,T$^{-1}$, in agreement with experiments,
with the BE variations of different complexes being very similar. Our results
will help identify charge complexes in the PL spectra of 1L-semiconductors
