You are correct!!

Sentence:  The audience burst out in applause, clapping their hands as the play came to a close.

This sentence is correct because we are talking about the audience as many people instead of one, making the plural pronoun their the correct use for this sentence.





5)  Adam and Christopher went in the back yard to play with his new truck.

   
a)  This sentence is correct.
   
b)  This sentence is incorrect.