Hello and welcome to fishforum! Congrats on the new betta, I'm sure he will be a happy and long-lasting friend.
If he's hiding, it's probably for a reason. I'm guessing he's stressed out, so moving around the tank right now will probably only stress him out more.
What are your water parameters? Ammonia, nitrite, nitrates? Since you say it's a new tank and he's been in it for 5 days I'm guessing that your water has built up ammonia and nitrites, which is making him sick. Have you done any water changes? I'd recommend testing your water and THEN doing a 50% water change.
Also, 70-80 degrees is a big temperature swing. I assume it's because you have an incandescent light in the hood which is causing the temperature to swing drastically? A lot of those small tanks do. He should be at a constant temperature of 78-80 degrees, as he is a tropical fish.
Here's a link to basic betta care. You can use it as a checklist to see what you've got and what you may be missing: