I havnt had my period on five weeks and give days exactly. Should I test for pregnancy? Also, reddish pink discharge 3 weeks ago, nothing since.

Absolutely. If you are sexually active ,yes.The home pregnancy test will provide you with an answer immediately.
Yes test. If you are sexually active, particularly so. It's hard to say what the reddish discharge meant as it could be related to a pregnancy but also related to the irregularity in bleeding that some women have with their menstruation. Remember it doesn't have to be a pregnancy causing this as many different things can lead to period irregularities.