I have an old keyboard I'd like to use on recent devices (no PS2 port). But it's still on a 5 pin din plug. I tried to plug that in a Din-2-PS2 adapter and that in PS2-2-USB, but the keyboard was not recognized at all. Is there anything I have to consider here? Should it work, or is there a reason why it cannot work?
There is a simple reason why it does not work. The keyboard does not talk the USB protocol.
With most mice and keyboards you have the following options:
The same is true for keyboards, though there are many more mice that support both PS/2 and USB than keyboards.
Now your keyboard has a old din plug. That means it is probably very old. Thus it is unlikely that it groks both the pre-PS2 din way and the modern USB method. This is why it fails.
If you want to get it to work you will need to add an active device which speaks both the old protocol and the new one. A mere plug which connects a few cables will no do.
And some convertors with active electronics inside them. These will work, even for old PS/2 keyboards. I never tested them with an additional AT keyboard plug.
DIN-5 used and PS/2 both use the same protocol, colloquially known as "AT". (in the case o PS/2, it's "ATX".) That's why the PS/2 is simply smaller, using a mini-DIN-6 connector instead o a DIN-5
Please note that really old keyboard (early 1980's keyboards), though using the 5-DIN connector, used the older XT protocol, so it probably wouldn't be compatible.
As far as the computer is concerned, there shouldn't be any difference between a PS/2 keyboard and a DIN-5 keyboard with a PS/2 adapter. So either the adapter is malfunctioning, or something isn't working on the USB side o things.