Thank you for the opportunity to help you with your question!
1. To take the 'log' of a number, it must be greater than zero. You can look at the graph to see that the 'log' graph is never a negative x-value, or you can try taking the 'log' of a negative number in your calculator, and it should come back undefined. So you can set the inner part of the log greater than zero.
So, domain is: (5,infinity)
2. For all cubed roots, there are no restrictions to the domain. It's a simple rule you can just memorize. The reason this works is because you can multiply three negative numbers with each other to get a negative number, so the inner part of the cubed root can be negative. The inner part of a square root cannot be negative though.
Domain: (-infinity, +infinity)
Please let me know if you need any clarification. I'm always happy to answer your questions.
Domain for e^x is all real numbers, so (x+4) can equal anything. No restrictions on the domain. You can also see from the graph that the domain of x is (-infinity,+infinity). The range, however, is limited.
For the first two, there are no other values of x that would cause the function to be undefined.