Does Irelia Fervent still become a 5 Might when readying at the beginning of turn?

Yes, Irelia, Fervent will become 5 Might if she is exhausted at the start of your turn during the Ready Step (formerly the Awaken phase).

According to RiftJudge FAQ #236:

• The Trigger: During the Ready Step, you ready all exhausted game objects you control. Because you are the one readying her, this satisfies the condition of her ability: "When you choose or ready me, give me +1 Might this turn."
• The Result: If Irelia was exhausted, she is readied, and her ability triggers, granting her +1 Might. Since her base Might is 4, she becomes 5 Might for the turn.
• Important Nuance: If Irelia is already ready at the start of your turn, she cannot be readied again (Rule 415.1.b), so her ability will not trigger, and she will remain at 4 Might. Additionally, this only triggers if you are the one readying her; if an opponent's effect readies her, it does not trigger her ability.