Actually,I don't know how to run firefox in init5 via the termimal.

If you wish to run a graphical program like Firefox, then you need to be running X windows.

The SERVER can be in "init 3" (no graphics), but you can run Firefox remotely (by using vncserver, or by using an X emulator and setting $DISPLAY on your remote PC).

Conversely, your server can be in "init 5" (graphics mode) ... but if you <Ctl-Alt-F1> to a text-only virtual console, then you CANNOT run Firefox (because your logon console has no graphics).

Bottom line: if you're sitting in front of an X Windows logon, then you can run Firefox (whether your X windows is local or remote). If you're sitting in front of a text-only logon, then you can't.

It's as simple as that

Well, you can run firefox from a text console if you tell it which X display to use. Of course, this requires a running X display. Here's what I did:

1. Boot into runlevel 3 (text console); log in
2. startx (starts X; display is :0)
3. Alt-F2 to bring up a new tty; logged in as the same user as in step 1
4. firefox --display :0 firefox is opened on the X display

Not sure if this is what you were asking for

Another idea (WRT opening graphical apps on an alternate X display/from a text-mode tty) is to set the $DISPLAY variable before running the command, e.g.:

The advantage to this is that it doesn't rely on the program needing to have some kind of display-setting option/switch.