Hi Mark,
According to this documentation: http://h17007.www1.hpe.com/device_help/H3C-manuals/miscellaneous/HPASeriesSwitchesBrandMigrationFeatureGuide.pdf H3C S5820X have been renamed to HP A5280X.
So, I guess that the latest firmware available for your device is here: https://h10145.www1.hpe.com/Downloads/SoftwareReleases.aspx?ProductNumber=JG243B&lang=en,en&cc=us,us&prodSeriesId=4177501
One of my customer has A5800-24G-SFP (JC103A) Distribution Switch that were bought during HP/H3C merge and below are the firmware installed:
<BA-E4-D06-A_SWDIS>dis dev man
Slot 1:
DEVICE_NAME : A5800-24G-SFP JC103A
DEVICE_SERIAL_NUMBER : CN28BFR00W
MAC_ADDRESS : B8AF-67F2-69DB
MANUFACTURING_DATE : 2012-08-11
VENDOR_NAME : HPE
Power 1:
DEVICE_NAME : NONE
DEVICE_SERIAL_NUMBER : NONE
MANUFACTURING_DATE : NONE
VENDOR_NAME : NONE
Power 2:
DEVICE_NAME : NONE
DEVICE_SERIAL_NUMBER : NONE
MANUFACTURING_DATE : NONE
VENDOR_NAME : NONE
Fan 1:
DEVICE_NAME : NONE
DEVICE_SERIAL_NUMBER : NONE
MANUFACTURING_DATE : NONE
VENDOR_NAME : NONE
Slot 2:
DEVICE_NAME : A5800-24G-SFP JC103A
DEVICE_SERIAL_NUMBER : CN28BFR002
MAC_ADDRESS : B8AF-67F2-61F2
MANUFACTURING_DATE : 2012-08-11
VENDOR_NAME : HPE
Power 1:
DEVICE_NAME : NONE
DEVICE_SERIAL_NUMBER : NONE
MANUFACTURING_DATE : NONE
VENDOR_NAME : NONE
Power 2:
DEVICE_NAME : NONE
DEVICE_SERIAL_NUMBER : NONE
MANUFACTURING_DATE : NONE
VENDOR_NAME : NONE
Fan 1:
DEVICE_NAME : NONE
<BA-E4-D06-A_SWDIS>dir flash:/
Directory of flash:/
0 -rw- 32949 Mar 31 2017 16:13:16 config.cfg
1 -rw- 33 Mar 31 2017 16:13:12 system.xml
2 -rw- 79295 Mar 31 2017 16:13:12 config.cwmp
3 -rw- 29491 Apr 04 2016 04:34:29 _config_bak.cfg
4 -rw- 10483002 Mar 31 2017 03:03:28 logfile.log
5 -rw- 31853568 Mar 16 2016 15:44:20 a5800_5820x-cmw520-r1810p01.bin
6 -rw- 27443204 Feb 28 2013 15:35:45 a5800_5820x-cmw520-r1211p09.bin
7 drw- - Feb 13 2013 17:45:32 config_archive
8 -rw- 27368692 Nov 18 2011 14:22:38 a5800_5820x-cmw520-r1211p01.bin
9 drw- - Apr 26 2000 12:00:34 seclog
515712 KB total (418846 KB free)
<BA-E4-D06-A_SWDIS>dis boot-l
Slot 1
The current boot app is: flash:/a5800_5820x-cmw520-r1810p01.bin
The main boot app is: flash:/a5800_5820x-cmw520-r1810p01.bin
The backup boot app is: flash:/a5800_5820x-cmw520-r1211p09.bin
Slot 2
The current boot app is: flash:/a5800_5820x-cmw520-r1810p01.bin
The main boot app is: flash:/a5800_5820x-cmw520-r1810p01.bin
The backup boot app is: flash:/a5800_5820x-cmw520-r1211p09.bin
So, I suppose that this firmware: https://h10145.www1.hpe.com/Downloads/SoftwareReleases.aspx?ProductNumber=JG243B&lang=en,en&cc=us,us&prodSeriesId=4177501 is the correct one.
Just in case you worried about "breakin" the device, there is nothing to worry about, as you can configure a backup boot firmware and if the main firmware you install is not compatible, the switch will tell you at boot time :-)
Hope that helps.
Jean-Christophe