Ophelia has fallen into madness following the death of her father. In scene 5, do her statements and singing suggest she is only disturb by his death or something else troubling her?

Ophelia's statements and songs definitely show that she is mourning her father "he is dead and gone lady", but they also show that her rejection by Hamlet has been troubling her. Many of the songs she sings include lyrics about how untrustworthy young men can be.

This passage, especially, shows that she is thinking about Hamlet:

"Young men will do't ... they are to blame.

Quoth she, before you tumbled me,

You promised me to wed.

So would I ha' done, by yonder sun,

An thou hadst not come to my bed."

This song refers to a young man who made a promise to a woman, and then broke it. This mirrors her relationship with Hamlet because he gave her letters, tokens, and promises, told her he loved her, and then threw all of that back in her face and said she was a fool for believing him.