Signal requires Android 4.4 or better. Essentially any Android device meeting that requirement, which isn't so locked down that it allows you to install software (from the Play Store, APK sideloading, whatever) will be sufficient.
The Nexus 5 is 8 years old now. (The age is a particular problem given its lack of replaceable battery.)
You can find used budget smartphones from 3 - 4 years ago for about $20 and they will have far more performance and capability.
From a security and privacy standpoint, you should probably run a recent operating system. That's a tricky one with smartphones, Android is rarely maintained properly by the hardware manufacturer for long. A device supported by something like LineageOS or similar would be good to look for.
As a starting point, the budget Motorola series (Moto E, Moto G series) tend to have small screens, large batteries, and unlocked (or unlockable) bootloaders, often with maintained LineageOS ports.
