(oo=inf)
Limx-->+oo (5^x - 7^x)
Believe or not, when I plug it into my computer software, it comes back with this succinct message:
(no interesting limit points found)
Here's a graphical solution: https://www.desmos.com/calculator/f7c6wqsvxl
Note....as x grows larger and larger, the value of 7^x is much greater than 5^x......so......this function approaches [ -inf ] as x grows sufficiently large
Thus......the limit does not exist