Will Premiere Pro run on my AMD Ryzen 5 4500U for 1080p/24fps video editing?

I know this is old, but others will come across it as I did. This article from AMD should answer your question about hardware encoding for exporting video:

https://community.amd.com/t5/gaming/create-videos-faster-on-the-go-with-amd-ryzen-mobile-processors/ba-p/414188

As far as the processor and other specs go, my daughter is currently editing and exporting 1080p videos for her high school news "broadcasts" on her HP Envy x360 laptop that has a Ryzen 4700U (with integrated graphics like yours), 16GB of RAM, and an SSD that's no more than half the size of yours. She loves it and says that it works great for everything she does in her video editing with no hiccups from 1080p source material.

I tried to do my best to make sure that what I bought for her in 2020 was up to that task, because she showed a lot of interest in video editing when she was learning to do it at her old high school then. There are plenty of reviews for AMD's processors from that year whose testing shows what they can do. I assume that processors introduced in the years since are even more capable.

For anyone looking at this in the future, it seemed like this computer's specs could allow it to do 4k editing, but it also looked like it would probably be pretty sketchy at it. When I gave it to her, I told her to avoid trying to tackle 4k video, because this processor didn't seem to have the horsepower for it. From the information that I was finding online, it seemed that 1080p was the real limit of what it could do well in terms of editing. I'm happy to report that this seems to be the case. 

Not well at all, I'm afraid. AMD Radeon GPUs of the GCN (pre-RDNA) generation, including yours, have historically performed extremely poorly in Premiere Pro. What makes this even worse is that integrated graphics processors that lack its own discrete RAM (outside of those in Apple-silicon Macs) tend to choke very badly in Premiere Pro, even with 480p (SD) video content!

On top of that, in addition to an integrated graphics that's utterly horrible for GPGPU processing, the integrated AMD Vega graphics does not have hardware decoding or hardware encoding capabilities at all whatsoever. This forces all video processing onto your already-underpowered CPU.

As a result of all that, your PC will perform worse in Premiere Pro than even a cheapo Intel-powered dual-core i3 CPU-powered laptop, let alone a proper 6-core CPU-powered laptop with a decent discrete GPU. Worst of all, your CPU's six cores cannot multithread at all (or put it this way, has single-thread-only processing). So 6 cores but only 6 threads. Not enough horsepower these days for any sort of video editing.

Moved to the Video Hardware forum.

Download the trial and give it a spin.