Which two numbers will be on faces that touch both the 1 and the 5 once this net is made into a cube?

Find the opposite pairs first. In the row 5 2 4 the end squares are opposite: 5–4. 1, on the far left of the top row, folds round opposite 2, and 6 is opposite 3. A face touching both 1 and 5 can be neither of them nor their opposites 2 and 4, which leaves 6 and 3.