If you have infinite life, can your life total be set to a specific number?
There is a ruling on this already in gatherer. You said it was rule 119.5 but it is also a ruling on this card. So in this situation your life becomes 5 at the end of each turn regardless of being set to infinity because of life link.

If an effect sets your life total to a specific number, it will be that number, even if you previously had infinite life.

The other gather ruling even makes reference to the ruling that is right below it which I have listed above.

If you give Infinity Elemental lifelink and it deals damage, you will gain infinite life. You might think infinite life sounds like a lot, and you’d be right. Once at infinite life, your life total mostly can’t change (see below). At infinite life and gain 2 life? You’re at infinite life. At infinite life and lose 29 life? You’re at infinite life. You can pay any amount of life and still be at infinite life. In fact, if you’re at infinite life and get with an opposing Infinity Elemental, you’d still be at infinite life.