Purism's Librem 5 and Facebook's WhatsApp – a curious combination! Yes, that's possible. There is more than one way to do this:
1. The most pain free way – leave it all up to Purism. They will take care of everything. At least, I presume they do this too. You have to pay for it though. I think it's about 8 euro per month for their full software support package. Now, normally, the kind of software they offer is already totally free anyway, but if your time is more precious than your money, then this will make life easy for you. Actually, this is quite good value. For example, if you choose the paid version of a good email service such as Tutanota, it's €12 per month. Purism provides a full package. Matrix is part of that package, and that can communicate with WhatsApp by 'bridging' (look at the Matrix website).
2. The normal way – install WhatsApp onto your device (only available on Google/Open Android, Apple iOS, Apple Mac and Microsoft Windows. Either wait for Facebook to make it available to your operating system of choice, or install Android onto this device. Then open an account on WhatsApp if you don't have one already in order to communicate with other WhatsApp users.