Filling and root canal filling 5 days after princess lip filler. Will I be okay?

If your having any planned dental work close to having a aesthetic treatment, you are often best to wait. The swelling is likely to have gone down, and there are no issues with having more local anaesthetic. The main concern would be if the filler moved due to the pressure on the lips, for example stretching the mouth to get access to the root canal. At 5 days the capsule is quite soft around the filler so it can still move with high pressure, which may happen.
I recommend waiting till after the dental work is done just to make sure you get the best long term result from the filler

Good afternoon.  Thanks for your message.  I feel 5 days might be cutting things close if you tend to swell or bruise when you have filler treatments.  This could compound discomfort for your dental procedure.  I would recommend 7-10 days prior to dental procedures if possible.
Thanks and wishing you the very best.