To express the number 5931 in Roman numerals using an extended notation system, where a bar or overline represents multiplication by 1000, the number can be broken down as follows:

1. 5000: Represented as ‘V̅’ (where ‘V̅’ signifies 5000).
2. 900: Represented as ‘CM’ (‘C’ is 100 and ‘M’ is 1000, but in this subtractive combination, it represents 900).
3. 30: Represented as ‘XXX’.
4. 1: Represented as ‘I’.

Therefore, 5931 in extended Roman numerals is written as: V̅CMXXXI.

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