Hello OP,
I was in Malta in May (8 hours on a cruise) and I think you can easily keep busy for 5.5 days. Valota is a fascinating city and Malta is a varied island. There's a saying that Malta has never owned by the Maltese. Malta is the crossroads of different cultures: drive on the left like the British; good morning, good afternoon and good evening is spoken in French (or is it Italian?); thank yous are in Italian (or is it French?); counting is in Arabic. English is widely spoken. Valota is built like a fortress -- because it had to be.
Malta is the most remote island I've seen with a nice size population.
You will have a great time.
David