Suppose that a player has Alhammarret's Archive in play, and has Read the Runes with X=5 resolve targeting them on the opponent's end step. Does that play have to discard any cards or sacrifice any permanents, and, if so, how many?

Read the Runes X

Instant

Draw X cards. For each card drawn this way, discard a card unless you sacrifice a permanent.
Alhammarret's Archive

Legendary Artifact

If you would gain life, you gain twice that much life instead.

If you would draw a card except the first one you draw in each of your draw steps, draw two cards instead.