I have two computers, both have Firebird 2.5 installed. The firewall is disabled in both computers. I am trying to access the database on the other computer using FireDAC Connection Editor, but I get the error:
Failed to connect to DBMS !
[FireDAC][Phys][FB]unavailable database
I tried different configurations, but I always get the same error.

Your "Database" path will not work, it is a network share, and Firebird doesn't open databases over network shares, so it won't be able to use that path. A Firebird server must be running on the remote host, and you need to connect through that database server, using a filepath local to that server.
In addition, the file seems to be located in a user directory. Unless you're running Firebird as an application (using the account of that user), Firebird will not have access to files in a user directory. The file needs to be in a location where the user running the Firebird server process has read and write access.
Also, I'm not sure what options are offered under "Protocol" (I don't program Delphi nor use FireDAC), but "Local" doesn't sound right either (I'd expect something like TCP/IP).
So, change your configuration so "Database" contains the local path of the database file on the server (or an alias configured in aliases.conf), "Protocol" has the right value, and "Server" contains the right host name or IP address of the remote server.