What category ethernet cable does it come with? (Cat 5e, Cat 6 etc)

I don't remember to be honest but probably 5e. Depending on what you're doing either one will work.

Questions & Answers: Refurbished: ASUS EA-N66 1 x RJ45 for 10/100/1000 BaseT Dual-Band Wireless-N900 Gigabit 3-in-1 AP / Bridge / Range Extender

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ASUS EA-N66 Dual-Band Wireless-N900, 3-in-1 Access Point / Repeater / Gigabit Ethernet Adapter IEEE 802.11a/b/g/n 1 x RJ-45 Ethernet Port Up to 450 Mbps Downlink + 450 Mbps Uplink Wireless Recertified

IEEE 802.11a/b/g/n
Up to 450 + 450 Mbps Wireless Data Rates
2.4 GHz / 5 GHz
WPA2

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