The date of this, the famous "Electric Lady" concert, was long believed by many collectors to have occured on December 5th, 1974. However, there is much evidence that the performance in fact took place on December 22nd and a complete lack of evidence of Rush performing on December 5th.
Multiple sources imply that the Electric Lady show was one of the last, if not the last concert before Fly By Night was recorded. Based on the below published accounts, it is unlikely that the Electric Lady concert took place in early December; most likely the concert was closer to Christmas and the recording of Fly By Night in early January:
1) During a performance recorded for radio at the Agora Ballroom in Cleveland on December 16th, Geddy states:
"We'd like to do a song right now that's going to be on the next album...matter of fact, it's also the title of the next album. It's a song called 'Fly By Night'. It's a song we wrote a couple weeks ago, and it's the first time we're playing it right now."
2) The timing of this concert in relation to the recording of Fly By Night was confirmed in "Circus Raves" magazine:
"...after a WQIV-New York radio concert, and five days off, Rush entered the studios to record their second, far more satisfying album, Fly By Night." - Circus Raves, November 1975
3) The timing of this concert, and the subsequent recording of Fly By Night is also discussed at length in Visions, summarized here:
"Just before Christmas Cliff Burnstein set up an important radio concert for the group in New York City. Rush's gear was set up in Jimi Hendrix's Electric Ladyland [sic] Studios. The show was broadcast live over WQIV to Big Apple rock fans...Besides giving the group radio time in New York, the show gives a good sound picture of the band, just a few months after Neil joined and before they hit the studio for the second album." - Visions
4) And lastly, the official 1974-1975 retro tour t-shirt produced by the Rush Backstage Club in 2002, which included many dates from 1974 which were later confirmed as accurate, lists "Dec. 22 New York, NY" but does NOT include December 5th in its listing.