I have yet to actually get my rating up to 5 stars as whole (probably because I was getting so many 4 star reviews for so long since I didn't know how to achieve 5 star ratings), but I have been consistently getting each customer to give me 5 star ratings and it's not as difficult as I thought it would be. I wanted to share because I know how frustrating it can be to experiment futilely!
I have two playable sims with max vet skills and full perks. I cheat to keep their needs fully met so I can keep the vet clinic open indefinitely but that is probably not necessary. The key is really in @Cupid's post - make sure you have a few decorations that boost environment by your check in and before you great the patiently warmly, let the the guests notice the decor. A small square with a picture frame inside will appear over the patient's rating star if you let them hang out in the area for a short while and when that disappears, that's when I click on the patient to greet them. That almost always boosts them from a 3 star to 4 star before you even start examining, and I've found that it doesn't matter how many tests you run or how long it takes to examine the pet, if you give the correct treatment at the end, you end up with a 5 star review. I have found that calling a pet a "good pet" never seems to have an effect on the rating and sometimes it even inexplicably lowers it so I leave that out. I allow one or two patients on my lot at a time since I have two vets and then I just repeat the process. Hope that helps lower some of the frustration!
EDIT: Literally just after I posted this, I got my clinic up to 5 stars, so it does work! :)
