I hold the same interpretation as Pax on the St. Malachy prophesy.
I also have a hypothesis about what happens after.
In the Apocolypse, ch14, vs 6, Three angels make various declarations. The last angel warns against taking the mark of the beast.
In the first few chapters of Revelation, the bishops of the seven churches are referred to as angels. I think the third angel is Peter the Roman condemning the mark in the last days of his papacy. Since all three declarations are like ultimatums, they are all probably in the decline of the period of peace.
We also have the prophecy of Don Bosco about two popes who rally the Church to a decisive victory at the end of the world, and the prophecies that reference the angelic pastor who will work with the great monarch. There is probably some overlap amongst the various sources, but there should be at least three after the 5th age.