The blue-straggler binary WOCS 5379 is a member of the old (6-7 Gyr) open cluster NGC 188. WOCS 5379 comprises a blue straggler star (BSS) with a 0.42 Mo white dwarf companion in a 120-day eccentric orbit. Combined with the orbital period, this helium white dwarf is evidence of previous mass transfer from a red giant. Detailed models of the system evolution from a progenitor main-sequence binary, including mass transfer, are made using the Modules for Experiments in Stellar Astrophysics (MESA). Both of the progenitor stars are evolved in the simulation. WOCS 5379 is well reproduced starting with a 12.7-day period binary with a primary star of initial mass 1.19 Mo, whose core becomes the white dwarf. The secondary star initially is 1.01 Mo. 300 Myr ago, the secondary finished receiving mass from the primary, having moved beyond the NGC 188 turnoff as a 1.20 Mo blue straggler. Key Findings: 1) The successful model has a mass transfer efficiency of 22%. Non-conservative mass transfer is necessary to avoid common-envelope evolution. Non-conservative mass transfer also is key to expanding the orbit to long period. Long-period orbits are typical for blue stragglers, and so perhaps is non-conservative mass transfer. 2) The mass transfer begins with a short unstable phase, during which half of the accreted mass is transferred. 3) The evolution of the progenitor secondary star into a BSS is primarily one of interior re-structuring in response to increasing mass. 4) Upon completion of the mass transfer the interior structure of the BSS matches that of a 1.21 Mo star with an age of 2.1 Gyr, which is at the same location in the HR diagram as the BSS. 5) The previous finding suggests that use of single-star models to determine BSS masses may have some validity; however, the use of such models for dating BSSs is not valid. 6) The formation ages of both stars in WOCS 5379 is the age of the cluster, 6-7 Gyr. However, the mass transfer creating the BSS occurred only 300 Myr ago, which we call the transformation age. Finally, the evolution age of the BSS is 2.1 Gyr. The next goal is similarly detailed production of an entire cluster BSS population. This will require further development of the physics of the stable mass transfer process with attention to the processes of stellar rotation (as yet not included), the nature of system mass loss, and orbital eccentricity evolution, along with complementary understanding of common envelope evolution. The authors acknowledge funding support from NSF AST-1714506, ACI-1663696, and AST-1716436 and from WARF. EML is supported by an NSF Astronomy and Astrophysics Post-Doctoral Fellowship under award AST-1801937.