Depends upon what you refer to as "really old" (yeah, I fit that category!); the oldest I-5 segment in the LA area is actually that stretch immediately south of the East LA interchange, dating from 1947. The portion along the LA river -- more or less from the 110/Pasadena freeway north to the 134/Ventura freeway, was completed between 1957 and 1962 (I grew up a couple of miles' distance from the 5/134 interchange).
Technically, you're correct about the name of the interchange. The actual East Los Angeles is an unincorporated area extending from the eastern LA city limits along Indiana St. east to Montebello, and between Monterey Park to the north and about Whittier Blvd. (pre-1953 US 101) on the south end. Pretty much everything south of Whittier is part of the City of Commerce. The one freeway-to-freeway interchange that is situated within the ELA zone is the junction of CA 60 and I-710. But the L.A. area interchanges have been blessed (or damned) with nicknames, most of which are part of LA traffic-reporter lexicon. The ELA interchange (5/10/60/101) got its name early, primarily from being east of downtown -- as well as one of the major focal points of cross-metro traffic. Of course, the original "named" interchange was the 4-level (101/110); the other east-of-downtown junction is the "San Bernardino Split" where the spur of I-10 west of I-5 terminates at US 101; although that interchange predates the northern I-5/I-10 interchange by about 12-13 years, the short distance between them -- as well as the fact that both of them involve the San Bernardino Freeway (I-10), both have, from time to time, received the reference of "San Bernardino Split". Derogatory names include the I-405/I-605/CA 22 interchange near Seal Beach; this has been given the term "Malfunction Junction" (sometimes used in other metro areas as well for complex interchange layouts). And, finally, down Santa Ana way, there's the infamous Orange Crush (I-5/CA22/CA57), complete with its U-turn ramp from EB 22 to NB 57 -- ironically, one of the most heavily-utilized rush-hour movements at that location.
When I lived in the L.A. area in the 2000's, occasionally I would hear the 60/710 interchange referred to as the "710 Stack" due to its multi-level configuration. But I've never heard Dan Faigin's fave, the 101/405, referred to by anything that would be printable in a family publication!