Mrthfx

In the exercises of thirds instead of playing it 1/3 2/4 3/5 can I play it 1/3 2/4 1/5 or it's not advisable? It's really hard for me to raise the fourth finger when going to play 3/5; are there exercises for that part to make you easily move from 2/4 to 3/5 smoothly and legato?

I'm new to piano, so I apologize if this is a silly question.

All fingering is flexible!

BUT, in a passage of 3rds, confined to the '5-finger position' you need a pretty good reason NOT to use 1-3, 2-4, 3-5. And 'I'm a beginner, and I find it hard to lift my 4th finger' isn't a good reason!

It sounds as if you're playing an exercise that covers that problem already! Stick with it. Check with your teacher that your arm, hand and finger positions are correct.

Whatever you are playing on piano, it is important to plan out the fingering so that you get the articulation you want and are able to get to what follows easily. The exact fingering is going to be dependent on the context of the piece, in combination with what works for your hand. It is advisable to try out different fingering options to decide what is best.

Take a look here as an example - Chopin, Etude #6 gis-moll. This is just a reference, there are a couple of ways, I think Liszt had his own way. As another reference, you can take a look at Czerny's 'The Art of Finger Dexterity', op 740 #10

Fingerings are suggestions, but in exercises they might be the whole point

When you learn a piece and you can do better with another fingering than the one on the piece, feel free to change it. Those are only suggestions.

With an exercise, on the other hand, the point is to learn how to do things that are hard. Of course, if you play it with a different fingering, you're still playing the same tune, and might even be playing it better (i.e. it sounds nicer), but the point of an exercise is not to sound good, but to help you learn. You might totally miss the point of the exercise by changing the fingering. Of course it also depends on the exercise itself - if the point isn't to teach you fingerings but legato/staccato or whatever, it might be harmless to change from the fingering.

Use the fingering as given in this exercise

In this particular case especially, I'd advise you to use the one that is given:

"It's really hard for me to raise the fourth finger when going to play
3/5; are there exercises for that part to make you easily move from 2/4 to 3/5 smoothly and legato?"

The anser is yes, it's the exercise you're doing right now, and it will only help you learn it with the fingering as written.

A very long time ago, I took piano lessons briefly.

I collect memory gadgets. The piano teacher knew this, and she gave me one: NARF. Notes, Articulation, Rhythm, Fingering. You want to think about ALL of these.

This sounds like a practice exercise, as opposed to a piece. It is designed to get you to the point that you can finger what you need, when you need it, how you need it. As such, it is worth the effort to work on it, as written, 1-3, 2-4, 3-5 and all.

The point in training particular fingering systems is to have a repertoire of standard fingerings working well together that can be applied without thinking. That does not mean that they will result in the unambiguously anatomically best total way to play any piece, merely that they will quite likely result in a feasible way to play it and will be well-suited to avoid "painting you into a corner" when sight-reading.

When you are training for a marathon and your trainer gives you a route, there is little point in finding shortcuts for that route. Even though for most real-life routes there may be corners you can cut, sometimes you will not have the time for finding those corners on a particular route, and being able to go the full distance will make the difference.

Carl Philip Emanuel Bach offers always different fingersettings and if he didn’t ... I would! Because I think the purpose to be be able to play a piece in a comfortable way and enjoy playing is as important to train the independence of each finger. Not every piano player has the aim to become a professional pianist. The joy of making music should be in a positive balance with finger training.