How did EMIYA experience his own Fifth Holy Grail War?
What we know from his past is that he tried to save Ilya but failed and he sacrificed his humanity to become a hero. I'm aware that EMIYA does not possess any specific memory from his Grail War but how do you think did the events occur? Was there an EMIYA already or did another Heroic Spirit take the Archer-Class?
There was always an EMIYA. He exists outside of time.
It is theorised that Rin summoned Ajax in the HGW that he participated in as Shirou. That would explain his knowledge of Rho Aius