A search for the axioelectric absorption of 5.5-MeV solar axions produced in the $p+d\rightarrow \rm{^3He}+\gamma(5.5 \rm{MeV})$ reaction was performed with two BGO detectors placed inside a low-background setup. A model independent limit on axion-photon and axion-nucleon couplings was obtained: $|g_{Ae}\times g_{AN}| \leq 3.2\times 10^{-9} (m_A=0)$. Constraints on the axion-electron coupling cons