More expensive = better?

You have to compare apples to apples. Price can reflect things such as built-in DAC card, phono section and/or headphone. The casework can add extra cost (engraving, anodizing, finish, CNC artwork, etc.).  Also, if it is sold direct it's about half the price a dealer would charge. Can't really generalize an answer on a dollar for dollar basis with respect to sound quality.

always

as in, 100% percent of the time

😉

I’d humbly propose widening the lens.  Assuming legit manufacturers, etc, a $150,000 preamp+amp(s) combo will always sound better than a $5000 integrated.  It just will, even to the most jaded among us.  Sure sure, you could have your quips, but it won’t be a serious comparison.  So, in a sense, “a lot more expensive” usually does sound better.  Turning to the OP’s specifics, comparing an $8000 amp to a $5000 amp could be pretty much like comparing a Coke to a Pepsi.  (Except without the decades of history proving that Coke is better.)

I think about it in categories, just as a rough guide.  5-10k amplifiers, for example, are all on the same footing.  Use your ears.  5 v 20?  Decent chance 20 wins.  5 v 50?  I’d bet a chunk of cash that 50 wins.  

All other things being equal, intuition would suggest that an amp costing $8,000 would be better than an amp that costs $5,000.

Keep it simple.  Its not like choosing Coke or Pepsi you know.

Assuming legit manufacturers, etc, a $150,000 preamp+amp(s) combo will always sound better than a $5000 integrated.

I would agree with this. Personally I don’t think you need to go up to $150k worth of preamp+power amp to beat a $5k integrated. A $50k pre power should show a $5k integrated a clean pair of heels. Having said that, to me, a quality integrated starts somewhere at $7k, new prices. The higher you go the better it sounds but one has to pick carefully, of course. Aspects such as preferences,  point of diminishing returns etc. will be applicable.

As mentioned earlier, some amps may be disguised to look $8k but sound like a $2k.