No, this is good. BUT something you really need to learn is how to write proofs. You can't just have a string of equations, you need some words to glue the equations together. A common mistake with beginners is that they don't do this.
Your proof is correct of course, but try to put some work in presenting it. How I would write your proof is:
Our goal is to prove that 5x-3 is odd for even integers x. So, assume that x=2a. If we substitute that into 5x-3, we get
5x-3=10a-3=10a-4+1=2(5a-2)+1
So, we have shown that 5x-3 has the form 2n+1, where n=5a-2. Hence, 5x-3 is odd.
As you see, this proof is quite longer. But it much more pleasant to read! In fact, if you search research papers, you will often see long strings of text with occasionally some symbols and some equations. This is the way mathematical texts should be written...