We're going to be taking a side trip to the Lauterbrunnen Murren area for 5 days. Does anyone know if it is possible to send luggage to the Bern rail station via the train and have them keep it for 5 days? Or other options for leaving luggage for multiple days in Bern until we get there? We'll be staying in an Airbnb so we can leave it there.
from swiss stations to other swiss stations, very normal. Storage at destination station on Arrival day and following 4 days included in price (and arrival is 2 days after sending so your 5 days should fit your plan).
https://www.sbb.ch/en/offers/luggage-transport-station-to-station