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In 5k the k represents thousand comes from the unit prefix "Kilo-", which in the metric system denotes a multiplication of the unit by one thousand. The word Kilo- in term comes from the Greek word χίλιοι (chilioi), meaning thousand.
I believe in latin "kilo" means 1000, k is short for kilo.
In math Kilo is the metric prefix meaning 1000 times.
Kilo
Kilo- prefix means thousand, so to convert kilometers to meters multiply by 1000. 1 km = 1 x 1000 m