This is going to vary from county to county, I believe. Here's why I say that. While the process is just that of turning in your application again, to include any info that may have changed over your last 5 years, the application fee, and I believe a current passport photo. The normal process is people make an appointment to turn in their info and be screened. Then they get a call to come pick it up once the Sheriff Dept has run their info and it's "ok". However, If they are not busy or you have a friendly smile and they like you, I had a student walk in with all his info and leave that day. And, this was Franklin County. Rare, for sure. But, it can happen. And this was from scratch, his first time. Not a renewal. He took my class on a Saturday, and text me a pic of his CHL that Monday morning. I would have called BS otherwise. He had no legal issues and his paperwork was in order.
That's the 1%. 99% of us, I would expect 3-5 day turnaround after turning in our. info. County to county will be very different.