OP at the end of the day you can collect internet opinions all you want but only you know her and whether this strong preference for an expensive bauble paid for entirely by you is a one off thing or indicative of other financial issues.
Personally I skipped the engagement ring and we got married with $20 rings from Amazon so I'm not one to understand the joy of expensive jewelry but...
1. Skipping an engagement ring did lead to a lot of social pressure - mainly on my now husband. I quite happily announced "I'm cheap, I said I didn't want one" and everyone who knows me found that easy to believe. I think he worried more that people thought it was him being cheap when they asked and found we didn't get one.
2. Weddings are weird and do weird things to people. I can completely understand why she doesn't want to chip in to pay for her own engagement ring. I'm not saying it makes sense but I could see it really not being easy to tell people that your husband didn't value you enough to pay for the ring you really wanted and so you paid for half yourself. Of course that's not what you would say... but it's how it would come across to a lot of people.
I'd say talk, talk and talk some more about it with your fiancee. The money isn't really the main issue, it's how she's going to feel about this. If that particular ring is really what she has her heart set on and you want to marry her then, since you can actually afford it, then I think you should. But I'd be more curious to know what it is exactly that is driving her desire for a Costco ring of all things.
At the end of the day $5000 is nothing compared to the cost of marrying the wrong person (read some of the threads on here where people talk about the cost of their divorce if you want some stories) and so I think understanding her thinking is much more important that the cash.
+1 (emphasis added as well)
This is a frugal board. Of course you're going to get a lot of people here advising against it. Let's agree - this is not the most frugal move! Regardless, it may still be the best decision.
People here are quick to attack things that aren't their gazingas. If they travel, they attack those living in HOC area. If they spend money on their children's education (and woe betide one who pays for an ivy league college education rather than making the kid pay), they attack those spend their money on travel. And so on.
Kamingoe is right. Figure out if this is a one off, or if this is indicative of a difference in values. If it's a difference in values, you've got a lot more thinks to coming. If it's a one off, only you can decide if it's worth it - if she really wants it, it's very sentimental to her, she'll wear it every day as her only piece of jewelry, etc. Talk to her.
But the other posters are right that you may change your mind about biglaw or not get that plum job. I had friends that happened to them. So consider compromises. There's no need to postpone a wedding over a ring you can't currently afford though. Why not agree to $100 rings now, until after you start your biglaw job full-time. Then when you have the income to afford it, replace it. Use the $100 ring when you travel and you may be worried about safety. For the $100 ring, consider something quite sentimental - friends of mine made each other rings in a jewelry studio which looked really awesome. (Btw, don't get $1k rings then upgrade to $5k rings!)
ETA: I will confess that I turned down a family ring, which is not the most frugal move. My MIL offered us her ring and DH & I both wanted to decline it. I'm not normally a "karma" person, but since her marriage ended *extremely* poorly and DH still has a bad relationship with his dad, I didn't want that to remind me whenever I looked at my ring. So you may get a great bargain at
https://www.idonowidont.com/, but you may want to make sure she's comfortable with it. An anonymous ring is likely better than a family ring with known really bad history.