There are \({5 + 7 \choose 5} = 792\) ways to get from the origin to \((5,7)\)
Now, we need to subtract this from the number of ways to get form the origin to \((4,4)\).
There are \({4 + 4 \choose 4} = 70\) ways to get from the origin to \((4,4)\).
So, there are \(792 - 70 = \color{brown}\boxed{722}\) ways.
Here is a link that explains this better: https://betterexplained.com/articles/navigate-a-grid-using-combinations-and-permutations/