Is the SolarEdge SE5K compatible with the BX51100 (5.12 kWh)?

Yes — listed by the manufacturer.

The manufacturer's published pairing data lists these together.

Minute Solar records SolarEdge SE5K with BX51100 (5.12 kWh) as compatible (A — Automatic). Derived from recorded specifications or compatibility groups; no manufacturer approval is recorded.

▦Manufacturer's compatibility listListed together in the manufacturer's published pairing data. A cited document reference is being added as datasheets are processed.