  Big Bang Nucleosynthesis (BBN) relevance reactions 3He(2H,{\gamma})5Li,
3H(3He,{\gamma})6Li, 5Li(n,{\gamma})6Li as a key to approach for scenario of
6Li formation are treated. The rates of reaction for these processes are
analyzed. Comparison of the reactions rates and the prevalence of light
elements leads to the assumption that the two-step process 2H + 3He --> 5Li +
{\gamma} and n + 5Li --> 6Li + {\gamma} can make a significant contribution to
the formation of 6Li at the BBN at least at temperatures T9 of the order of
unity. Calculations of the total cross sections, astrophysical S-factor, and
reaction rates have been performed for 3He(2H,{\gamma})5Li radiative capture
within the modified potential cluster model with forbidden states, which follow
from the classification of the orbital cluster states according to Young
diagrams. Numerical data and corresponding parametrizations cover the energy
range up to 5 MeV and temperature range T9<10. An updated compilation of
detailed data for the reaction 3He(2H,{\gamma})5Li are presented.
