A gaming system costs $600 and is on sale for 35% off. After the discount, there is a 5% tax. What is the final price of the gaming system?

The discount on the gaming system is 0.35 * 600 = $<<0.35*600=210>>210

So the gaming system now costs 600 - 210 = $<<600-210=390>>390 after the discount.
The tax adds 0.05 * 390 = $<<0.05*390=19.5>>19.5 to the cost of the gaming system.
Therefore, the final price of the gaming system is 390 + 19.5 = $<<390+19.5=409.5>>409.5. Answer: \boxed{409.5}.