Bad oil pressure? Is it just a clog somewhere? or a new pump is required? I'd get a second opinion if possible before deciding.
If I were you, I'd run engine flush a few times first. LiquMoly has a good reputation. I used it on my car without any problems. When I took off my upper timing chain cover last month, the engine looked very clean and new!
Also, how much can you buy a 2013+ A5 for in your market? 2013+ engines are supposed to have fixed most of the engine-related issues (i.e. tensioner, timing chain, intake manifold, HPFP, etc.)
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It looks like you've made some modifications to your car. So if you've already put in a lot of money into it, and you trust your friend to do a good job, then I'd just swap out the engine. Used car prices are crazy expensive now anyway.
Used car prices in the U.S. are crazy because most people who don't buy/sell used cars for a living rely on a "blue book" value for what they consider a fair price. Problem is, people don't know that blue book was bought out by a used car company year ago.
Therefore, people are essentially looking to an used car seller for how much they should pay for a used car. So it's no wonder that the used car seller says that the used car should be very expensive. It's such a conflict of interest that it should be illegal.
Quick note , in my 2.0t when I lost oil pressure it was my rear main seal gone , easy enough for self repair if you can get another pair of hands at the end to lift the gearbox back up , or even use the recommended gearbox jack mount solo
Ok by "bad oil pressure" do you mean the damage done by faulty lubrication has broken your engine so badly that it is no longer servicable? Or is your oil light coming on and your engine still runs ok? Is it smoking? I'm assuming you are in the US there are lots of salvage outlets here. You may have more choices than you know.
$8k is a lot for an engine. I just saw a pulled late model 4.2 Liter RS5 V8 for $10 k. Shop around at salvage yards. Don't wait for the engine to hit the market place. The 1 or 2 engines on Ebay are not the only ones out there. Find an A5 carcass and dicker for the engine. Or....Your car shows very well, find out what salvage value on yours would bring you might net out cheaper by selling your non running body for $4K (if you can) and buying a working replacement for $9k (if you can). Don't be discouraged. There is more than 1 way to skin a cat.