The Librem 5 will have the i.MX 8M Quad 28nm SoC, which contains four Cortex-A53 cores. Here are the only benchmarks that I can find for this SoC:
https://boundarydevices.com/nitrogen8m-android-benchmark/
You can compare the CPU in the i.MX 8M Quad to the Snapdragon 425 which was released in 2016, but the i.MX 8M Quad isn’t as power efficient, and it doesn’t have a dedicated digital signal processor or image signal processor like the Snapdragon 425:
You can compare the Librem 5 to a Moto E5 Plus, which also had 3 GB of RAM.
However, the specs of the SoC don’t tell the entire story. The Librem 5 will be running Linux/Wayland/GTK+/phosh, which should be more efficient and require less processing cycles and RAM than Android which runs everything in a Java Virtual Machine, so its interface speed will probably be decent and it should be capable of driving an external 1080p monitor with no problems.
As a computer programmer, I know that modern SoC’s have plenty of processing power, and benchmarks aren’t that important at the end of the day. You generally don’t see the difference unless you are comparing two phones side by side. Where you will probably see a difference is in the speed of the camera. For everything else, you won’t have the kind of software, where it is that important to worry about the SoC performance. Only if you plan on doing some intense desktop work when using an external monitor or somebody decides to make an app that runs Doom are you likely to notice the performance of the SoC.
At this point, we don’t know the camera specs, so it really premature to speculate about the Librem 5’s camera and video performance, but I wouldn’t plan on it being too good. The other area where the Librem 5 probably won’t be that good is in battery life, so you will probably have to charge the phone every night.
However, the Librem 5 will be able to do other things that other phones can’t. No other phone is able to run Linux, Coreboot and work on 100% free software, which means that your software will be supported forever, whereas Android phones only get 2 - 3 years of software updates. No other phone will allow you to run a Linux desktop. No other phone has an SoC which has 10 years of support from the manufacturer and gives you a M.2 slot so you can replace the cellular modem, plus replace the battery, so the Librem 5 could potentially last 10 years. If you think of it that way, the SoC in the Librem 5 is pretty good.