Stupid question first but is the oil level correct? As if the oil pump sucks even a little air it will loose pressure.
Here is a TIS for how to check the oil pressure with a gauge if you have the kit available. That would rule out the oil pressure sensor. Or alternatively they range from £4 up to £22 for a new one.
https://www.newtis.info/tisv2/a/en/e...supply/C4d3A3s
But the oil pumps on the older M57 were prone to failure but not too hard to change. You’d be looking at £200 ish for a Pirberg one or £90 for a Febi-Bilstein one. I’d get the best one you can afford tho! Plus gaskets, sealant and some new oil. Can be done on the driveway on a e39 5 series so will have loads of room to move under the e53.
https://www.newtis.info/tisv2/a/en/e...-motor/C49bznQ
And just hope that driving it with low oil pressure hasn’t screwed any bearings.