Option 1: Uttar Pradesh -> Shares a border with Nepal in its northern region.
Option 2: Bihar -> Shares a border with Nepal along its northern frontier.
Option 3: Assam -> Located in Northeast India, does not share any border with Nepal.
Option 4: Sikkim -> Shares a border with Nepal on its western side.
Hence, Option 3: Assam -> Assam is situated in the northeastern part of India and is geographically separated from Nepal. The five Indian states that share borders with Nepal are Uttarakhand, Uttar Pradesh, Bihar, West Bengal, and Sikkim -> correct