In total, Ann and Dan have 180p + 400p = 580p, so they need to end up with 290p each. Therefore Dan needs to receive at least three five pound coins from Ann to have enough money. Then, Ann has 250p, so she needs at least two two-pound coins from Dan, at which point they have £290p each. Therefore, at least 5 coins must change hands.
This problem is taken from the UKMT Mathematical Challenges.