Where does fate/destiny occur in Act 1, Scene 5 of Shakespeare's Romeo and Juliet, and how is the involvement of fate/destiny expressed?
The events that occur in the play are really a mixed result of both fate and personal choices. Scene V of Act I is one scene in which we see fate involved, but only after Romeo makes his personal choice, against his better judgement, to join his friends in crashing the Capulet ball.
We see Romeo allow himself to be swayed by his friends in the previous scene, Scene IV, even though Romeo feels crashing the ball is a bad idea. In this scene, Benvolio and Mercutio try to persuade Romeo to join them in crashing the ball because they feel it will lighten Romeo's mood and distract him from being love sick over Rosaline. Benvolio is particularly hoping to distract him from Rosaline. However, Romeo is extremely reluctant to go. He says he will carry a torch to light their way, but he is "too sore enpierced with [Cupid's] shaft" to dance (I.iv.20). He further says that he is reluctant to go as he feels a sense of foreboding; he actually prophesies going to the ball will bring the consequence of his early death, as we see in his lines:
I fear, too early; for my mind misgives
Some consequence, yet hanging in the stars,
Shall bitterly begin his fearful date
With this night's revels and expire the term
Of a despised life, clos'd in my breast. (I.iv.113-117)
While choice brought Romeo to the ball, fate is responsible for not only introducing the lovers but also keeping them divided. Hundreds of people are present at the ball. It is not a matter of coincidence that the two saw each other and nobody else. In addition, fate is responsible for their parentage. It is due to fate that Juliet was born a Capulet and Romeo a Montague, two families that happen to be warring with each other. Juliet refers to the involvement of fate best when she says:
My only love, sprung from my only hate!
Too early seen unknown, and known too late!
Prodigious birth of love it is to me
That I must love a loathed enemy. (I.v.147-150)
Not only does her phrase "[p]rodigious birth of love" refer to the fated beginning of her love life, it also refers to her fated birth as a baby, showing us that fate is responsible for both Romeo and Juliet being born into the families they were born into.