The most common and most likely answer to this crossword clue is the 5 letter word QUIPU
I've seen this crossword clue in The Guardian
Q
U
I
P
U
More clues leading to the result QUIPU
Buddy explains!

The straight part
We know that "Old mnemonic device" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old mnemonic device = quipu.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does QUIPU mean?
QUIPU noun- A recording device, used by the Incas, consisting of intricate knotted cords.