This Sanskrit root panca for "five" is related to the Greek pent- root that we see in English words like pentagon, pentagram, etc.
In the traditional Indian game of pachisi, played with cowrie shells, twenty-five was the highest throw of the shells, hence the name. In modern parcheesi, which is played with dice, five is still an important number in the game because pieces move into play when you throw a five.
Although the Indian game is supposed to be quite ancient, the oldest testimony for the game dates to the 16th century. Legend has it that the Emperor Akbar of India had a courtyard in the shape of a pachisi board, with members of the harem acting as the pieces.
In the ancient Indian epic, the Mahabharata, there is a dice game which is crucial to the plot. The description of the game in the epic does not seem to correspond to pachisi, but modern artists have imagined that the game was indeed pachisi, or something very much like it, as you can see in this 19th-century illustration:
The first American version of the game was called Patcheesi and a copyright claim was filed in 1867. The name was later changed to Parcheesi, and the North American rights are currently held by Hasbro. The Parcheesi board game shown below is from Wikipedia:
For more about games in India, see this article: Ancient India, The Birthplace of Modern Game Design.