Rule 119.5 states
If an effect sets a player’s life total to a specific number, the player gains or loses the necessary amount of life to end up with the new total.
The ruling on Infinity Elemental states
If an Infinity Elemental you control gains lifelink and deals damage, you’ll then have infinite life. From that point on, your life total effectively can’t change. If you lose life, you’ll still be at infinite life. You can pay any amount of life and still be at infinite life. In fact, you can be hit by an opposing Infinity Elemental and still be at infinite life.
On one hand, "the necessary amount of life to end up with the new total" seems to indicate that I must end up at 5 life, but the ruling seems to indicate that not even an infinite loss of life can change my life total (infinity minus infinity being mathematically undefined aside). Which one controls?