Mbappe, who scored a hat-trick in France's defeat by Argentina in the World Cup final just over a month ago, netted a hat-trick in the first half here as PSG led 4-0 at the break against their regional league opponents.
The striker struck twice more after the restart, with Neymar and Carlos Soler scoring PSG's other goals in the last-32 tie.
No player had ever scored five times in a single competitive match at PSG. However, Kylian Mbappe scored five goals in fewer than 50 minutes against sixth-tier Pays de Cassel in the French Cup.
In addition, the France international is also close to another club record: all-time top scorer. Edinson Cavani scored 200 goals in all competitions and Mbappe has already scored 196 goals.