One unknown
Let my age now be $x$. So Granny's age is $4x$.
Five years ago, I was $x-5$ years old and Granny's age was $4x-5$.
At that time, she was five times as old as I was and so $$4x-5=5(x-5)\\
4x-5=5x-25\\
4x+20=5x\\
x=20$$
So Granny is $80$ and I am $20$, which means that the sum of our ages now is $100$.
Two unknowns
My age now: $m$
Granny's age now: $g$
$\therefore g=4m$
My age five years ago: $m-5$
Granny's age five years ago: $g-5$