There are two answers to this question:
Yes. Using the same 5V supply as the Arduino will work. HOWEVER, you will NOT HAVE ELECTRICAL ISOLATION – which is THE reason I included the opto isolators.
You might need to replace D1 with a plain piece of wire, as I count on it to take 0.7V out. but I’m guessing this won’t be an issue.
No. I included a separate, isolated, power supply on purpose. This is necessary if you want true electrical isolation between the ‘real world’ and your Arduino board (Strongly Recommended!)
So, there you have it. You pays your money, and you takes your chances.
BrianV