It is your obligation to light a candle, and say the blessing, every Friday evening.
The mitzvah of Shabbat candles applies to men and women equally.1 However, for several reasons (see Why is it the woman's role to light the Shabbat candles?) the rabbis instituted that if there is a woman (over the age of bat mitzvah) in the house, she should be the one who fulfills the obligation for the entire household.2
If there is no woman in the house, then the obligation falls upon the man.3



My grandfathers wife recently passed away. Is he allowed to light shabbos candles with a brocha? As well as must he light 5 candles for his 3 kids, his wife in remembrance and 1 for himself?
I am sorry for your family's loss.
Not only is your grandfather ALLOWED to light Shabos candles with a bracha, he is OBLIGATED to if he doesn't have a wife doing it on his behalf. He can choose whether to light two candles or the same amount his wife would light.