We will be staying five full days. Would it be cheaper to purchase a 7 day metro card?
If you're going to be going all over Manhattan, you'll be better off with a 7 day unlimited card. The bus/subway is $2.50 per trip so even if you only take the subway 2x/day, it will cost you $25 each. At least with the 7 day unlimited, you don't have to worry about running out and you can take the bus or subway as much as you need/want to.