Spells and abilities that cause the enchanted player to gain life still resolve while Grievous Wound is on the battlefield. The enchanted player won't gain life, but any other effects of that spell or ability will still happen.

If an effect says to set the enchanted player's life total to a number that's higher than their current life total, that player's life total won't change.

Grievous Wound's last ability triggers and resolves after the damage is dealt. For example, if the enchanted player has 10 life and is dealt 1 damage, that damage will reduce their life total to 9. Then Grievous Wound's ability will cause that player to lose 5 life, leaving their life total at 4.

Grievous Wound's last ability triggers only once whenever enchanted player is dealt combat damage, no matter how many creatures deal combat damage to them at the same time.