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

Believe or not, when I plug it into my computer software, it comes back with this succinct message:

(no interesting limit points found)