Well...10GBASE-T could be deployed - for short reach (less than 55 meters long end-to-end) - using existing Cat.6 cabling...but Cat. 6A (or, even better, Cat. 7) should be the way to go to avoid troubles and nasty issues on longer runs.
Apart from that, did you tried to update the HPE FlexFabric 5700 software version to the latest one available (Comware 7.10 R2432P01)?
I ask because an interesting reading about failures on speed negotiations against a device with Smart Rate enabled ports with an HPE FlexFabric 5700 involved: software version plays a role (read this).
Are you referring to something like HPE (Aruba) Smart Rate?
From the Aruba Smart Rate Solution Overview document (here):
"HPE Smart Rate is a new multi-gigabit (1, 2.5, 5, 10Gbps) twisted-pair network interface that is interoperable with the NBASE-T ecosystem of 2.5/5Gbps products as well as with existing industry standard 1GbE/10GbE devices. It allows the majority of existing cable installations found in campus LAN environments to provide higher bandwidth connectivity, distribute PoE power to connected devices, and secure the wired-link for next-generation 802.11ac applications."
AFAIK only (some) Aruba Switch families - like the Aruba 5400R zl2 and the Aruba 3810 Switch Series - support it...and HPE Smart Rate technology should be compatible with Cisco Multigigabit Ethernet technology implementation (which is based on NBASE-T).
I'm not sure that actually Comware based Switches are supporting the HPE Smart Rate technology as (some) ArubaOS-Switch based ones recently do...so I think they can't interoperate fully with NBASE-T implementations and listed products (see www.nbaset.org)...but I could be wrong here.