You have the right three pins, and pin 5 is right.
Billy's Law of Serial Comms says, no matter how much you try to work it out in advance, you have a 50% chance of getting RxD and TxD the right way round.
Normally, TxD from the PC is pin 3, and must be connected, via an inverting level shifter, to RxD on the target board. So it looks to me like you've got pins 2&3 reversed. But by Billy's Law, I only have a 50% chance of being right!
I take it you have a suitable inverting transceiver, like a MAX232 chip between Arduino and PC, yes? The Arduino signals are all 0V-5V logic signals. RS232 from a PC is ±9V (or something in that region). Without a transceiver, it won't work at all.
If you're sure you have a good ±9V transceiver installed, then:
EITHER:
hook it up like that, if it doesn't work swap 2&3;
OR
With the DB9 not plugged into the PC, use a DVM to check that whichever of pin 2 or 3 is -ve (between -3V and -15V) on the PC, THE OTHER PIN is -ve on the DB9 cable end. If both -ve pins are the same pin number, swap 2&3.