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We develop a grand unified theory of matter and forces based on the gaugesymmetry $SU(5)_L\times SU(5)_R$ with parity interchanging the two factorgroups. Our main motivation for such a construction is to realize a minimal GUTembedding of left-right symmetric models that provide a parity solution to thestrong CP problem without the axion. We show how the gauge couplings unify withan intermediate gauge symmetry $SU(3)_{cL}\times SU(2)_{2L}\timesU(1)_{L}\times SU(5)_R$, and establish its consistency with proton decayconstraints. The model correctly reproduces the observed fermion masses andmixings and leads to naturally light Dirac neutrinos with their Yukawacouplings suppressed by a factor $M_I/M_G$, the ratio of the intermediate scaleto the GUT scale. We call this mechanism type II-Dirac seesaw. Furthermore, themodel predicts $\delta_{CP} = \pm (130.4 \pm 1.2)^\circ $ and $m_{\nu_1} =(4.8-8.4)$ meV for the Dirac CP phase and the lightest neutrino mass. Wedemonstrate how the model solves the strong CP problem via parity symmetry.

Predictive Dirac Neutrino Spectrum with Strong CP Solution in $\pmb{SU(5)_L \times SU(5)_R}$ Unification