Actually, being pedantic, a 5 element lens will let in more light (strictly, pass more light) than a 12 element one at the same f stop. And two different 5 element lenses may differ in the exposure depending on aberration correction.
The number of air/glass surfaces, particularly internal is far more critical than the number of elements.
If we take 3 classic lens designs, the Dagor, Tessar, and Celor/Eurynar (Dialytes), all have 4 elements. The Dagor has 2 cemented cells and only 2 internal air glass surfaces, the Tessar has one cemented cell and 4 internal air/glass surfaces. The Dialytes have 4 air spaced elements, and 6 internal air/glass surfaces.
Some tears ago I test these lens types using macro bellows on a DSLR, all in excellent optical condition. As expected the Dagor was the best, the Tessar not bad, and the Dialyte noticeably lower in contrast. Of course these were uncoated lenses, but the light loss is not significant, less than 1/3 of a stop.
As soon as you add coating the difference becomes insignificant, contrast similar. However, when you multiply up the air/glass surface that changes.
Transmission Stop is used in Cinematography where complex zoom lens designs may have around 20 - 25 elements. Cooke did make uncoated Zooms bofore WWII, but they only really became practical with lens coatings. Cameramen needed precision for exposure, particularly when changing lenses, or multiple camera shots, so lens light transmission was measured rather than calculated, hence the T stop.
We take a lot of terms for granted, take Focal length, at one time a lens might be sold or marked as as E.F. (Effective Focal Length) or Equiv - Equivalent Focus (Focal Length). The easiest way to explain this is Telephoto lenses. I have an ex-military 17" f5.6 Telephoto lens, it had no f-stop markings, to do that I needed to calculate the Effective Focal Length, an easy calculation as it's - f-stop x Aperture diameter, in this case around 10".
My 360mm f5,5 Tele Xenar needs approx the same bellows extension as my 210mm f5.6 Symmar S, so in reality the Tele-Xenar has an Equivalent FL of 360mm nut an Effective FL of around 210mm, checking a Schneider data sheet the lens has a Flange focus of 210.3mm.
It gets more complex with many wide angle lens designs, for SLRs, and then zooms, In practice a great many lenses are marked with their equivalent focal lengths, which is all we are interested in as photographers
Ian