.....5 1/3' was initially put in to provide a 16 ' resultant against an 8'.....
Many years ago, I was checking out a small 3-manual Gress-Miles, which has a 5 1/3' in the Pedal. In an attempt to produce a 16' Resultant, I drew it and the 8'. All I heard were the two pitches together, ppppffffff!!
Unbeknownst to me at my young age, perhaps that wasn't G-M's or the organist's intention for the Pedal Quint.
In other cases, I've noticed it does very little or nothing to registrations I've heard, but that could have depended on what it was used with.
Next thing to come to mind is a CD I have, which was done at Sacre-Coeur by Daniel Roth. In one of the tracks, he demonstrates the 32'-series mutations, where, in this case, the 5 1/3' could be viewed as the 19th with the 4 4/7' "21st" right after it.
To be able to hear something effectively, it comes down to the voicing, placement and not to use it if you know it's going to be buried by other voices.
e.g. one wouldn't use a Flauto Dolce or an Aeoline with "English Swell" (Principal, Fourniture, Trumpets 16', 8, and 4') coupled to Great Diapason plenum and Tuba Mirabilis. Or add a 5 1/3' to a 16' Quintade, unless you have a thing for second harmonics.
Now, what does this have to do with the 64' Tromba, a thread about which
I started? lol Maybe I've watched too much Rosanna Rosannadanna years ago. lol The things we've been discussing seem to have two connections... acoustical effects of two or more pitches and what our ears detect, or miss.