TL;DR
use
hw_mode=a
I see that the man pages for hostapd are quite useless
I found a more useful page https://wiki.gentoo.org/wiki/Hostapd with the following example
802.11a/n/ac with WPA2-PSK and CCMP
A simple but secure AP for recent hardware:
FILE /etc/hostapd/hostapd.conf
interface=wlan0 # the interface used by the AP
hw_mode=a # a simply means 5GHz
channel=0 # the channel to use, 0 means the AP will search for the channel with the least interferences
ieee80211d=1 # limit the frequencies used to those allowed in the country
country_code=FR # the country code
ieee80211n=1 # 802.11n support
ieee80211ac=1 # 802.11ac support
wmm_enabled=1 # QoS support
ssid=somename # the name of the AP
auth_algs=1 # 1=wpa, 2=wep, 3=both
wpa=2 # WPA2 only
wpa_key_mgmt=WPA-PSK
rsn_pairwise=CCMP
wpa_passphrase=somepassword
with the useful comment
hw_mode=a # a simply means 5GHz
Please note: apparently later versions (v2.6+) of hostapd do NOT like inline comments in the config file