I've only heard the LCD-5 briefly and at Canjam, so I can't offer detailed comparative impressions. But I'll say they're really quite different headphones.
The LCD-R is closer to the older, warmer/darker Audeze tuning of the LCD-2, 3 and 4. The 5 is a significant departure from that old house sound, instead having a lighter tonal weight and a more neutral/bright sound. I found the 5 to be too up-front in its presentation, and too emphasized in the upper-mids/lower treble for my tastes (I'd go so far as to call it borderline shouty).
The LCD-R, by contrast, is more mellow. The bass rolls off more than the LCD-5, which has much better sub-bass depth. The R is more about mid-bass punch. Its bass is slightly thick and bloomy, more about texture than tightness/speed.
The R's treble is also slightly rolled off, contributing further to the warm tuning, which verges on sounding a bit closed-in at times.
The beauty of the R lies in its mids, which are rich and slightly wet. (People often described the LCD-4's mids as "liquid" and the same can be said for the R).
The overall sound of the R is very smooth but also lively and engaging, thanks to its snappy, fast transients. I can't remember if it's as snappy and fast as the LCD-5 but I remember the 5 as being more aggressive generally.
I'm not sure the R is a good replacement for the 5, if you like the sound of the 5. If you're looking for a different listening experience, the R could work well (as might the 4z). If you can swing it, having both would make for a good combination insofar as you'd have two headphones with contrasting presentations.