In Act V, we learn that Friar Laurence's letter is not delivered to Romeo due to circumstances beyond his control. He had asked Friar John to deliver the letter to Romeo, but he had been unable to do so because he was quarantined in a house due to an outbreak of plague.
The conflict in this excerpt is an external one, as the circumstances are beyond the Friar's control. It could be considered an example of man vs. nature (the plague) or man vs. fate.