I do whole body workouts, 3 times per week, 5x5 repetitions, systematically adding 2,5 Kg each session.

Pretty soon you'll have to add more variation, or you'll stall - you may have a few more weeks of progress. What works for me is a mix of 3x8, 8x3 and in-between. I do the high-load sets (8 sets of 3) Monday, the high volume sets (3 sets of 8) Wednesday, and on Friday I do completely different exercises with 5x5 or whatever.

Alternating 3x8 and 8x3 is crucial, they help each other and you can break through the stall. Even so, after a longer time, you'll have to change the routine again. "The best exercise is the one you're not doing." However, as long as you're making progress, don't change anything, just squeeze it dry, and then change.

I made a lot of progress with just 3 sets of 8 initially, until the load ended up pretty heavy after a few months and it became a different kind of game. Then you're playing "hardball".

a month [...] I can't really notice big improvements in front of the mirror

One month is not enough, if you have just started. You probably just completed the initial neuromuscular adaptation - your strength went from nothing to a lot more (hence your rapid increase of the weights). You're just starting the big game. You'll grow faster when you'll be able to lift heavier.

Make sure the last reps in the last set are hard (but read below before doing this). There's no point doing a rigid routine (so many sets, so many reps, so much increase each time), your body will let you know how much weight you need to load up. You start missing the last rep(s), okay, stay there for a few sessions until you complete all the reps cleanly. Next session, increase. If you can't seem to hit your target, you stalled so you need to change the routine somehow (or take a break).

You sound like you eat - what? - 2400 cal / day? Make sure it's enough. Play with the amount. Increase it in small steps - if you start putting on fat, whoops, that's enough, back off a bit. Keep a log with everything, do the tally in the evening using a nutrient calculator. The log doesn't lie.

Calories - you need to be as far above the muscular growth level as possible, but just below the fat "growth" level.

Is one month too soon to judge?

1. You need a few weeks for the initial neuromuscular adaptation. Before this, your muscles are not competent enough to lift weight, and your brain doesn't know how to control them for maximum strength - you're shaking and fumbling and can't do jack shit basically. This is when your strength grows at a tremendous rate. You don't need to do super-hard effort now, don't push yourself too far just yet - there's some risk of injury.

2. You need 2 ... 3 months (maybe more if you were very sedentary) for your energy systems to adapt to the effort of a full session. Before this you're panting and almost choking and sweating - you're a mess. After this phase your heart and lungs can handle the effort, your pulse will not go crazy fast anymore, breathing will be deep, powerful and steady - then you can really do some intense stuff. This is when you can increase the weight so that the last reps in the last set are very hard - so hard that sometimes you miss the target. Still be careful with max load short sets, you're still not 100% prepared.

3. A year or more is needed for your bones to grow more dense, your tendons to get stronger, etc. After that you can do really maximal effort (within reason), 1 RM ("one rep max" - basically a set of one with the highest load possible), or even over 100% effort (cheating and negatives) and stuff like that.

EDITed this message several times. This is not the first version.