Five-membered rings are constituents of many polycyclic aromatic hydrocarbons (PAHs), and their presence on the edges of large PAHs has been repeatedly observed experimentally. However, modern kinetic combustion models often do not consider the growth of PAHs through the transformation of the five-membered rings. In connection with the above, we carried out a theoretical study of the mechanism of hydrogen-abstraction-acetylene-addition (HACA) transformation of an embedded five-membered ring on the armchair PAH edge to a six-membered ring, considering cyclopenta[d,e,f]phenanthrene (4,5-methylenephenanthrene) as a prototype system for this process. The potential energy surface for the reactions of cyclopenta[d,e,f]phenanthrenyl radicals produced by direct H abstractions from cyclopenta[d,e,f]phenanthrene with acetylene has been compiled at the G3(MP2,CC)//B3LYP/6-311G(d,p) level of theory including zero-point vibrational energy corrections. The computed energies and molecular parameters were then used to solve the Rice-Ramsperger-Kassel-Marcus master equation in order to calculate the reaction rate at various pressures and temperatures, which were fitted to the modified Arrhenius equation for further kinetic modeling. The results show that the HACA transformation of the embedded five-membered ring to a six-membered ring is possible, albeit slow. The most viable reaction mechanism involves the R2 + C2H2 reaction, where the acetylene molecules add to a σ-radical in the six-membered ring adjacent to the five-membered ring via a low entrance barrier. The predominant product of R2 + C2H2 is predicted to be 3-ethynyl-4H-cyclopenta[def]phenanthrene Pr5 via immediate H elimination from the initial addition complex. Next, Pr5 undergoes H-assisted isomerization to 4aH-pentaleno[4,3,2,1-cdef]phenanthrene Pr4, and the latter adds a H-atom eventually forming the 1-pyrenylmethyl radical Pr3: R2 + C2H2 ⇆ 3-ethynyl-4H-cyclopenta[def]phenanthrene (Pr5) + H or 4aH-pentaleno[4,3,2,1-cdef]phenanthrene (Pr4) + H; Pr5 + H ⇆ Pr4 + H; Pr4 + H → 1-pyrenylmethyl (Pr3). This HACA sequence may be competitive with the methyl radical addition to the R1 radical formed by H abstraction from the CH2 group in the five-membered ring of cyclopenta[d,e,f]phenanthrene, which provides a pathway to pyrene following two H-atom losses. Relative contributions of the two mechanisms of the five- to six-membered ring transformation would strongly depend on the branching ratios of the R1 and R2 radicals produced by the H abstractions and the available concentration of C2H2 versus CH3 and hence differ in different flames.