Does a V5C show previous owners?

Only partially. The V5C shows the number of previous registered keepers and the date the last change happened — but it doesn't list their names or contact details for privacy reasons.

A vehicle history check can show more detail on keeper change history, including how many changes there have been and roughly when, which helps you judge whether the ownership pattern looks normal (e.g. one long-term owner) or unusual (e.g. several keepers in a short period, which can sometimes indicate an underlying problem with the car).