Can i put a battery operated fm transmitter in my computer?

You need to put four diodes to drop the excess 2 volts.

Dropping 3 volts from a 5 volt supply is easy. All you need
are 2 resistors in series across the 5 volt supply. resistor
number 1 is 247 Ohms and number 2 is 680 Ohms. Both
resistors are 1 Watt at 10% tolerance. You can get your
3 volts across the 680 Ohm resistor. It will be close enough
to operate your little transmitter and your resistors shouldn't
get that warm to worry about. You could also use a 1,000
Ohm potentiometer, too. Connect your 5 volt supply across
the element (pins 1 & 3). The wiper (pin 2) is where you will
get your 3 volts from. Pin 1 is common ground. Pin 2 is your
3 volts. Pin 3 is your 5 volt supply connection. With a volt
meter connected to pins 1 & 2, adjust the potentiometer
so the meter reads 3 volts. Once this is done, you can go
ahead and connect this supply voltage to your X-mitter.

As for noise suppression, that is not an easy task. Insulate
the X-mitter w/ tape. Allow for your input, power & antenna
wires. Wrap this package in foil. Ground this foil to the case.
You will have a little interference, but that can't be helped.
The closer the receiver, the less interference. Route the
antenna outside of the case, if possible,

I cannot guarantee success of interference level at this point.
You can try it. Feel free to e-me.