2,4GHz antennas are compatible with 5GHz connection?
I have a laptop that I would want to upgrade the wireless device with
  a new one that operates at 5GHz


Assuming that you mean that you want to upgrade/replace your "wireless router" and not the internal laptop electronics.


  my question is if the antennas used for 5GHz connections are the same
  as for the 2.4GHz, or I'll have to change antennas with new ones.


The correct answer is: it depends

There are mono-band antennas, which are only for 1 band, and there are multi-band antennas which may do more than 1 band.

Usually, antennas on "wireless devices" are mono-band, and would only handle one band.

If you edit your question with more details and specifications of the equipment your are using now, and the equipment you are planning, then I will edit this answer with more precise info.

[EDIT-based on edited question]

You may want to check if your Laptop "allows" you to swap the Realtek out for another card. Many laptops have "white lists" in their BIOS, which may or may not be user configurable. I would advise you to double check this with the laptop manufacturer prior to buying anything.

Question is now on hold, so I will not be further updating this answer.