802.11ac with a 2.4GHz router

I'm looking to get a new computer for someone and am trying to understand 802.11ac. It only runs on 5GHz according to everything I've seen, so my question is, can it connect to an older router that only works on 2.4GHz (like a Linksys Wireless-G router)? Can the 802.11ac PC use 2.4GHz to connect, say at a slower speed like N? Or would the 802.11ac client be incompatible with a router that only works on 2.4GHz?

If this is a dumb question I apologize, but I can't find a straightforward answer anywhere. Thanks.

Yes, 802.11ac ONLY works on the 5 GHz band, but:

802.11ac is backwards compatible with 802.11n and other "legacy" standards

802.11ac falls back to 802.11n to serve devices which don’t support it. This works very similarly to how 802.11n falls back to serve 802.11b/g and 802.11a clients nowadays.

802.11ac is therefore backwards compatible with 802.11b, g and n. This means you can buy an 802.11ac-equipped device and it will work just fine with your existing router.

Backwards compatibility is a key point since nearly all deployments will be dual-band and therefore will need to support 802.11n for years to come.

EDIT:

Some devices may only be capable of 5GHz, which means they’d only be able to revert to 802.11n. So if you want to maximize compatibility with older standards, be sure the Wireless Card of your new PC is dual-band.

You're absolutely right that 802.11ac is only defined for operation in 5GHz. However, because compatibility with older 2.4GHz-only gear is so important, all 802.11ac gear I've ever seen also supports b/g/n in 2.4GHz.

So if you have an 802.11ac client card, it will switch to 2.4GHz b/g/n mode to connect to an old 2.4GHz-only AP (wireless router). And if you have an 802.11ac AP, it's actually "simultaneous dual band" which means it's two APs in one box at the same time. One is a/n/ac in 5GHz, and the other is b/g/n in 2.4GHz. So your legacy 2.4GHz-only gear will connect on 2.4GHz.