So I spent some more time looking into it. Couldn’t find one leak on or around the springs. The hissing has to be coming from somewhere around the engine, as it’s only audible when I turn off the car.

Looks like I’ll just have to be patient and wait for my pump repair kit and diagnostic set to arrive (might take a while with the full lockdown here) and then look at it further. Luckily it’s still usable.

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03.06 BMW X5 4.8is LeMans Blue