Where Roman numerals are used?

Answer 1

They were used throughout the Roman Empire (primarily Europe and Western Asia) and were in common use for a long period after its demise, even after the introduction of Hindu-Arabic. It wasn't until the 16th century that Hindu-Arabic became the dominate numeric system in Europe.

Today, they are used wherever ordinal linguistics (first, second, third, etc) could be used, such as outlines and ordered lists, lineage (e.g., King Louis XIV), grand events (Olympic Games XXX), the hours of an analogue clock and the moons of a planet. They are also used to denote the year of a building's construction (e.g., cornerstones), and in musical notation to denote a progression regardless of key or the to mark the individual strings of a stringed instrument, as well as in chemistry to denote the various positive charges of an element, and in book prefaces and volume numbering (e.g., Lord of the Rings, Book II - The Two Towers).

Answer 2

Five different current uses for Roman numerals would be...
1) As numerals on clocks and watches.
2) As regnal numbers of kings and queen, for example King Henry VIII
3) The oxidation states of elements in compounds, for example Iron III oxide.
4) As dates, often shown in movie credits, for example MCMLXXIX (1979)
5) In Movie titles, for example "Star Wars episode VI: Return of the Jedi."