  We discuss the possibility to predict the QCD axion mass in the context of
grand unified theories. We investigate the implementation of the DFSZ mechanism
in the context of renormalizable SU(5) theories. In the simplest theory, the
axion mass can be predicted with good precision in the range $m_a = (2-16)$
neV, and there is a strong correlation between the predictions for the axion
mass and proton decay rates. In this context, we predict an upper bound for the
proton decay channels with antineutrinos, $\tau(p\to K^+ \bar{\nu}) \lesssim 4
\times 10^{37} \text{ yr}$ and $\tau(p \to \pi^+ \bar{\nu}) \lesssim 2 \times
10^{36}\text{ yr}$. This theory can be considered as the minimal realistic
grand unified theory with the DFSZ mechanism and it can be fully tested by
proton decay and axion experiments.
