For 10 points, give this shared name of popes, the fifth of which was pope during the fall of Constantinople and is known for his reconstruction of Rome and patronage of Fra Angelico and Leon Battista Alberti.
One pope with this name enlisted Richard I of Capua in order to do battle against antipope Benedict X, and an antipope with this name was made so by Louis IV and was the last antipope to be controlled by a German Ruler. Stephen Porcaro sought to overthrow another pope of this name.The fourth pope of this name sent John of Montecorvino abroad for missionary work and sought to renew another crusade after the fall of Ptolemais. The most notable pope of this name arranged for the Concordat of Vienna with Frederick III and employed both Nicholas of Cusa and John of Capistrano as missionaries. That pope of this name also issued the Dum Diversas papal bull and oversaw the construction of the Vatican Library.  For 10 points, give this shared name of popes, the fifth of which was pope during the fall of Constantinople and is known for his reconstruction of Rome and patronage of Fra Angelico and Leon Battista Alberti.
One pope with this name enlisted Richard I of Capua in order to do battle against antipope Benedict X, and an antipope with this name was made so by Louis IV and was the last antipope to be controlled by a German Ruler.
Nicholas