Here are my suggestions for your ABRSM Grade 5 exam.
I have chosen the pieces carefully so that you may give the best performance whilst also, (where possible) purchasing books that will contain other pieces that you may wish to play or even use in other future exams.
You can download the full syllabus here.
Purcell Rondeau (from Abdelazar)
Gershwin But Not for Me
Paul Harris Study in D.