I've been in the industry (developer for Finance, backend, quant stuff) for 5 years, and I was thinking to starting looking for a remote developer position in a couple of years.

Do you have any advice? Shall I start studying something? I'm proficient with C++, python and C#, but mainly for numerical algorithms, but I'm sure I can learn other stuff.

Don't.
Remote work doesn't work. I think it's even been scientifically proven. You can make it work if the whole team is remote and the company really focuses on remote work but 2 remote dudes in a team of 10 will never work.

Edit: I should clarify that it will work in that something does get done. But the efficiency of it is shite

@Froot That's true, but I'll also consider going to firms where everyone works remotely!

@7Raiden From my experience it works. But you must do a thorough look inward to see if it will work for you.

Do you live alone in a strange city without much as far as friend or family?

Do you have trouble not working during your off hours?

Do you have trouble working during your on hours?

If you answered yes to any of those, it's not a fit for you. First question - because you will be socially isolated and probably wind up depressed (happened with me earlier on in my career).

Second question - because you'll work yourself into a powder and burn out.

Third question - because you'll never get anything done.

Some tips (I successfully work from home, have for many years).
1. Have a dedicated area of your house you work in.
Only work there, ever. This will help you not work too much and not get distracted when you do.

2. Use your PTO / sick days.
You're not going to be productive those days anyway, otherwise you'll never use your PTO.

There are more but those are key

@codePatrol Yes I totally agree with you. The reason why I want to WFH is that I want to live in a city that I like.

Also, I'll either have a dedicated room (with a separate PC from my usual one) or I'll go to those shared workplace. Either one, I'll keep home separate from work.

As regards the actual work: I know the productivity is likely to be close to 0, but I sporadically work from home, and I have to say that I get things done (maybe because it's not an every day thing).

In terms of skills, I'm sure it won't take much to learn new techs, giving that I love to code, and I'm already familiar with OOP. Do you have any suggestions on the things I need to have on my CV?

@7Raiden Generally younger, bigger companies offer work from home but that's not universal. It depends more on the company than the job / technology. A job search for a remote position will be more competitive and harder to find but not undoable.

Another tip that I couldn't fit, don't be paranoid about going to the bathroom or taking lunch too. When I first started I was always nervous any time I was away from the keyboard. But you would be away from the keyboard at work as well when you hit the bathroom or got lunch, etc.

@codePatrol that's good advice thanks for that :)