Bringing it up is the right move, honestly. Five weeks is still early enough that you're figuring out compatibility, and this stuff matters - how someone spends their attention during time together says something about how they value that time. The longer you let it go without saying anything, the more you'll internally build a resentment story about it, which isn't fair to them or you.
The trick is framing it as a you thing, not a them thing. Instead of "you're always on your phone," try something like "I really enjoy our time together and I'd love it if we could do more stuff without the phones - like, just be present with each other." Most people respond way better when it doesn't feel like an attack. You're not being needy or old-fashioned; you're asking for basic presence, which is pretty reasonable.
If they get defensive or brushes it off, that's actually useful information about whether this person's capable of adjusting for someone else. But I'd bet they don't even realize they're doing it at the level you're noticing. A lot of people are just so conditioned to constant phone use that it becomes autopilot. Give them the chance to know it bothers you and see how they respond - their reaction will tell you a lot about whether this is worth continuing.