Brownish discharge during the 5th week of pregnancy can be caused by various factors and is not always a cause for concern. It could be due to implantation bleeding, cervical irritation, or even old blood from previous menstrual cycles. However, it is important to monitor the discharge and look out for any accompanying symptoms such as pain or foul odor. If you experience heavy bleeding, severe cramping, or have concerns about your health, it is recommended to consult with your healthcare provider for further evaluation and guidance. They will be able to assess your specific situation and provide appropriate advice based on your individual needs.