Chord starts with first key depressed and ends when last is released.
One-key chords: 5
One of 5 keys to press, one way to release key.
Two-key chords: 40
1 of 5 possible starting keys, 1 of 4 possible second keys, 5x4 20 openings.
With 2 keys held in, two ways to release: 1 of 2 keys to release first, 1 remaining key to release last.
A total of 40 (20x2) 2-key chords, 45 total chords so far.
3-key chords: 360(*)
5x4x3 for 60 openings. 1 of 5 first keys, 1 of 4 second keys, 1 of 3 third keys.
3x2x1 for 6 releases. With 3 pressed, 1 of 3 to release first, 1 of 2 to release second, last key released.
Total of 360 simple(*) 3-key chords.
405 (5 + 40 + 360) chords so far.
Yeah, biggest effort is not the hardware, but wiring the muscle memory, but I figure out motor system should be great at this if you're motivated.
(*) Simple chords - where we first just press and then just release, more options are available if we are ready to keep the sequence going by pressing and releasing and pressing again.
NOTE: Not original, this is my take on some one else's scheme, I'll look for the reference.