Five weeks. That's the answer, and honestly, it's not even a close call. For your first trip out of Australia, with Germany and Sweden as your anchors and free lodging with relatives, four weeks would leave you sprinting through the best parts. Five weeks gives you the breathing room to actually feel a place instead of just checking it off a list. You're not being indulgent by stretching it; you're being smart. The difference between "I saw Berlin" and "I got lost in Berlin and found a tiny karaoke bar" is exactly one week, and you want the second one.
Let's talk about what you're packing into those days. You mentioned cities, smaller towns, nature, hiking, nightlife, culture, lakes, and trains. That's a lot of different energies, and each one needs its own pace. Cities like Copenhagen and Stockholm are perfect for three or four days each, but you'll want a solid week in Berlin alone just to scratch the surface. The hiking and mountain time in Sweden's Lapland or Germany's Bavarian Alps isn't a weekend side quest; it's a reset button that requires travel days and recovery days. With four weeks, you're forced to choose between the nightlife and the lakes, between the culture and the mountains. With five, you can have both without feeling like you're cheating either one. Your relatives are a huge advantage here, not just for the free bed, but because they can show you the local spots that no guidebook covers. That's a superpower, and you should give yourself the time to use it properly.
The real trap is thinking that more days means more pressure to fill every hour. That's the opposite of what you want. Five weeks isn't about doing more; it's about doing less, but better. You can take a slow train through the Swedish countryside and just watch the lakes roll by. You can spend an afternoon in a Munich beer garden talking to strangers. You can decide last minute to stay an extra day in a small town because the vibe is right. That's the adventure you're actually after. The r/travel community often debates this exact question, and the consistent advice from folks who've done it is that the first trip is where you learn how you travel, not just where you go. You'll discover that you hate spending two nights in a row in hostels, or that you love waking up early for empty streets. Give yourself the space to learn those things without the clock ticking.
Here's your concrete takeaway: book the five weeks, but plan for only three of them. Leave two full weeks completely open, just a rough idea of which country you'll be in, and let your relatives and your own curiosity fill in the gaps. That's not a waste of time; that's the trip you'll remember. When you're back in Sydney, you won't say "I wish I'd seen one more cathedral." You'll say "I'm so glad I took that random Tuesday to hike that trail." That's the difference between a good first trip and an epic one. Now go tell your boss you need the time off.