Yes grapes do count as your 5 a day.
Other fruits that count as your 5 a day are bananas, pears, apples, canned fruit, 2 plums, 2 satsumas, 2 kiwi fruit, 3 apricots, 6 lychees, 7 strawberries or 14 cherries.
Basically as long as you eat any fruits then you will be eating towards your 5 a day goal.
All fruits are healthy for you so as long as you eat fruit daily or at least eat fruits most of the time you should be okay.
I eat at least a few types of fruits per day although I do not follow my 5 a day rule when it comes to eating fruit I just eat fruit when I feel like it.