Wi-Fi 5 is the consumer name for IEEE 802.11ac technology, while Wi-Fi 6 is the name for IEEE 802.11ax. Wi-Fi Alliance introduced the numbered names so people can tell generations apart without memorizing the IEEE codes: Wi-Fi 5 for 802.11ac and Wi-Fi 6 for 802.11ax.
Compared with Wi-Fi 5, Wi-Fi 6 is built for higher capacity and better performance when many devices share a network. It adds features such as OFDMA (sharing a channel among several devices at once), improved multi-user MIMO, 1024-QAM for higher peak rates, and Target Wake Time to help battery-powered devices sleep more efficiently (Wi-Fi Alliance).
Source: Wi-Fi Alliance: Wi-Fi (MAC/PHY) — Wi-Fi 5 and Wi-Fi 6
Image: Wireless access point, photo by Pjpearce, CC0, via Wikimedia Commons.