You can check this in the compatibility list. There you can see that the last supported models of the DX513 are from the 2017 series - officially.
Unofficially, they might work, but I wouldn't take the risk.
https://www.synology.com/en-global...
search_by=category&category=expansion_units&filter_hard_drive_bays=5%20bays&p=1
DX513 5 bays
17 series: DS1817+, DS1517+
16 series: DS916+, DS716+, DS216+, DS716+II, DS216+II, NVR216
...
DX517 5 bays
21 series: DS1621xs+, DS1821+, DS1621+, DVA3221
20 series: DS1520+, DS920+, DS720+
19 series: DS1819+, DS1019+, DVA3219
18 series: DS1618+, DS918+, DS718+, DS218+, NVR1218
17 series: DS1817+, DS1517+, DS1817, DS1517
