Unfortunately, I think not.
From what I can recall they were called the 5th Dimention (with the "t"), but were forced to change it for the obvious reason. They were from the NYC area, all in high school, I suppose (my father was, at least). They recorded this song (and maybe more?) for Columbia, but the label in the end only wanted to buy the song, not the band, and I guess it somehow fell through in the end. I believe there was supposed to be (or hoped to be) a string section added... Love-like.
I don't think my father has any of the other recordings, it they exist. But he does he have tapes of his other group the Yellow Jackets, who I think were more Seedsish, rather than Loveish---but I've unfortunately never heard them.... Too scared to handle 50-year-old reels. Of that group I have one nice photo, though.
If you other diggers want, I have a much higher quality transfer of this song I can share.