The real question is whether your bike's manual actually allows synthetic - because if Honda signs off on it, there's basically no downside to switching. Most modern bikes totally approve it, and your CB500F probably does too, but that manual is gospel. Once you've confirmed it's okay, synthetic genuinely does last longer between changes and handles the heat better, which matters even for weekend riders because heat buildup is heat buildup.
I switched one of my older bikes over to synthetic a while back and honestly the engine just runs smoother and cooler, which you can feel. The intervals stretched out too, so I wasn't scrambling for oil changes as often. For a CB500F doing casual weekend miles, regular mineral oil wouldn't destroy anything, but synthetic gives you better protection during those longer hot rides without much hassle. The cost difference evens out when you're changing less frequently anyway. Just grab whatever weight Honda recommends and make sure the bottle says it's approved for motorcycles - don't cheap out on random automotive synthetics.