In the opening monologues of Babylon 5 it is proclaimed to be the "dawn" of the third age of mankind, which started in 2257 with the founding of Babylon 5. What time periods covered the first two ages of mankind?
Sheridan and Delenn have a discussion at the end of B5:Into the Fire. They've just won the Shadow War and the Shadows and Vorlons (as well as the other Old Ones) have gone beyond the rim and left the galaxy:
JMS spoke about his desire to end on a slow note rather than an all-out battle specifically to indicate that we'd outgrown the need for intergalactic warfare;
The timescales themselves aren't well defined and would obviously be different for different species but it seems clear that the Shadows and the Vorlons have been at each other's throats for thousands (if not millions) of years, with various planets falling under their respective spheres of influence at different times.