Thanks for all the feedback!
After some careful fiddling, I can confirm that, for my machine, the GPU does not fit correctly into slot 1 because the processor cage is in the way.
My machine is 'mid-2012', single processor, MacPro 5.1 (Model A1289 / EMC2629)
The graphics card is Sapphire Pulse Radeon RX 580 8G GDDR5 with PN 299-1E387-000SA and SKU# 11265-05-20G (that's what it says on the box). Bought brand new.
I initially posted pics (above) of the GPU inserted in the PCIe slot at a steep angle. A number of people asked if I was sure that the GPU connecters weren't in fact underneath the PCIe slot, thus causing the alarming angle. I tried with the machine lying both vertically and horizontally, and carefully laying the GPU flat on the top of the processor cage, and visually confirmed, by looking through the empty slots above, that the GPU connectors were butting against the top edge of PCIe slot. See pic below.
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I confirmed that all the PCIe slots lined up correctly with the 'box/chassis' by trying different combinations of covers and PCIe devices. Everything seemed to line up correctly.
So then I pulled the processor cage out of the machine completely.
With the processor cage out, I then inserted the GPU into slot 1...and everything fitted perfectly. The card was at 90 degrees to logic board and the 'cable connections' part of the GPU fitting perfectly into the slot in the chassis. See pics below
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Once I had the processor cage out I thought that in fact it did not look perfectly 'square' and perhaps had a very slight 'bow', if I lay it on a flat surface there is a couple millimetres rock to it?
Gave everything a clean and put it all back together.
Tried inserting the GPU again and it was certainly improved but still a long way from 100%! See pic below
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I tried various combinations of removing screws from GPU backplate (side nearest PCie slot, both sides, none, removing springs from screws etc) and the best result (as seen above) was removing 2x 'springed' screws nearest PCie slot.
It requires a bit of force to get GPU 'level' and to line up so that cable connections are fitted to chassis properly and retaining plate screwed in.
This pressure is hinged directly on the GPU connectors which are in slot 1 - this is far from ideal
I booted up and everything appears to be running ok.
As far as I can tell, my options at this point are....
1. continue running with GPU forced into slot 1
2. remove backplate from GPU and fit to slot 1
3. fit GPU to slot 2 and lose access to slot 3
My final thought was to drill holes through the bottom of the processor cage and the chassis/box and insert bolts in an effort to try 'clamp' the processor cage downwards
Thanks for all the suggestions much appreciated !
Remove the plastic pad of the cpu cage