  We present a comprehensive study of an extended SU(5) grand unified theory
(GUT) that incorporates a 45-dimensional Higgs representation to address the
shortcomings of the minimal SU(5) GUT, such as the inability to generate
realistic fermion mass hierarchies and insufficient proton stability. By
considering a hierarchical mass spectrum for the scalar components of the
45-Higgs, we demonstrate that successful gauge coupling unification (GCU) can
be achieved. The color octet scalar, color triplet scalar, and color
anti-triplet scalar play crucial roles in realizing GCU when their masses are
significantly lighter than other components of the 45-Higgs. We focuses on the
proton decay channels mediated by the exchange of the color anti-triplet
scalar. Assuming that the 45-Higgs couples to all three generations of
fermions, we determine the 45-Higgs Yukawa couplings with which the observed
fermion mass matrices at low energies are realized. We calculate proton decay
rates using the Yukawa couplings obtained from renormalization group evolutions
and matching conditions at the GUT scale, thereby exploring the dependence of
proton decay rates on model parameters. We find that the $p \to \nu \pi$ mode
imposes the most stringent constraint on the mass of the color anti-triplet
scalar $M_{S_1}$. We also study the correlations between the lower bounds on
$M_{S_1}$ derived from different proton decay modes.
