Although 802.11ac is a 5GHz-only technology, I have yet to see an 802.11ac router that only supports 5GHz. All the 802.11ac routers on the market are simultaneous dual-band, so they do a/n/ac in 5GHz at the same time as b/g/n in 2.4GHz.
So go ahead and buy a simultaneous dual-band 802.11ac router, and your 802.11g NIC will see the router's 2.4GHz b/g/n network.