I wouldn't say that's normal, actually. Your iPhone 16 Pro should easily last you a full day with what you're doing. Five hours is not much, especially for a brand new device. iOS might actually optimize things a bit over the first few days, but it shouldn't affect your battery life that drastically.
Try checking which app is using the most battery. Go to Settings > Battery > Battery Health and see how the cell is doing; if it's already degraded (below 80-85%) your device might have a manufacturing defect. Disconnect from your home Wi-Fi for an hour and use mobile data instead, it could be that your phone is desperately trying to connect to something that's not working right. Restart your phone from scratch by resetting your network settings (it won't erase your data, just your saved connections).
If it keeps happening after all this, honestly I'd go back to the store or contact Apple. A week in and you're still under full warranty, and for such abnormal battery drain they have a duty to replace it for you. This isn't something you should have to fix yourself with updates.