Quote from: Psycopyro on September 11, 2021, 07:19:30 PM

As I understood, an private key starting with 5, give a legacy address only, and also give an uncompressed adress.

Yes. Uncompressed WIF keys start with 5 and should only generate uncompressed legacy addresses. You can use them to generate other addresses, but these address will be non-standard and it will be very difficult to successfully spend any coins sent to such addresses.

Quote from: Psycopyro on September 11, 2021, 07:19:30 PM

Obviously the public key generated by my 5xxx private key gave me a compressed key, probably compressed for ease of use.

You can use uncompressed private keys to generate both uncompressed and compressed public keys. Similarly, you can use compressed private keys to generate both uncompressed and compressed public keys.

Quote from: Psycopyro on September 11, 2021, 07:19:30 PM

Is there a way to find out our uncompressed key and perform send a transaction, just for science ?

You can use the latest version of bitaddress from here: https://github.com/pointbiz/bitaddress.org
Download, verify, and run offline.
Enter your compressed or uncompressed WIF key in the box under "Wallet Details", and it will show you both your compressed and uncompressed private keys, public keys, and addresses.