Your E5520 are 80W max TDP processors. You have the "Mainstream" heatsink/fan atop those.
The W5590 are 130 W max TDP processors. You would need the "Performance" heatsink/fan atop those, and the motherboard knows the difference. However, if HP never officially certified that W5590 as an approved processor for that workstation then it is highly likely that it will never run in the Z600 even if it "should" be able to.
Is yours a version 1 or versin 2 Z600? You can tell by looking up the boot block date in BIOS, System Info section.
You can research in here under:
Mainstream heatsink
Performance heatsink
Z600 and X5690 (similar to your situation but specifically for the version 2 Z600).