The latest version of GoGoD contains over 28,000 even games from the period since 2002 (roughly the 6.5 komi era). These yield us some 114,000 empty corners. We find more than 59,000 first plays on 4-4 and more than 52,000 on 3-4. Then we find about 1,000 on 5-3, about 650 on 3-3, and about 400 on 5-4 (from there we drop down to about 100 for first play on tengen). So even if we find some complete strategy explained for the latter three points (and I've not seen one), we should be aware that they have little general acceptance in actual contemporary professional practice. As always, however, that should not necessarily be an obstacle for us feckless amateurs.

I guess we will have to agree to disagree on this. Personally I think an observed 50-60 times difference in the choice of 4-4 and 3-4 over 5-3 requires a little more than 'not trendy' to explain it. Actually everything points to it not being a full value opening move, IMHO.

That seems to accord with the usual explanation that White often used 5-3 as a way of unbalancing the game in the days of no komi in particular.

(And of course Black can do the same if that suits his style.) The 5-3 is like an octopus, quietly sliding away along the sea-bed until attacked, whereupon it puts up a tangled web of tentacles. Its reputation for ladders might also be likened to a squirt of blinding ink. But its lack of pincering power makes it less forcing and less easy to integrate with other stones. Modern players prefer to be lobsters.