What nuclear symbol has 13 protons and 15 neutrons

It's simple.
The number of protons in an atom never changes. And also, the no of protons is its atomic number. If you look up the periodic table, you will find a number on the top - left corner of each of the boxes. This is the atomic number. No 2 same elements on the periodic table have the same atomic number. So, all you have to do is search for a box that has the number 13 on it.

and by the way ... the element which you're searching for is Aluminium.

It's an isotope of Aluminum so you would write "Al" with a "28" in the top left corner