Transportation from Tiberias to Ben Gurion airport

That depends on what is most important to you, time or money, and what other plans you have.

If your flight leaves at 5 AM on Saturday morning, you need to be there at 2 AM (it's recommended to come to Ben Gurion Airport 3 hours before the departure time).

This means that you can't use public transportation as it doesn't run on the Sabbath.

The simple and expansive option is to take a taxi, it would cost you somewhere around 900 NIS and would take 1.5 to 2 hours drive to get there. So you need to depart at around midnight.

If you want to save money, you can use public transportation to get closer to the Airport on Friday and then get from there by taxi, which would be much cheaper, for example, a taxi from Tel Aviv should cost around 170-180 NIS.

The cheapest option is to get to Jerusalem because it has a private shuttle service operated by Nesher Tours which costs only 40 NIS from the central bus station (according to their Hebrew site). You can get to Jerusalem from Tiberius by bus number 959, the last one leaves Tiberius at 15:00 from the central bus station and is expected to get to Jerusalem central bus station at 17:37. The problem with this option vs. Tel Aviv is that there aren't a lot of things open in Jerusalem on Friday evening and you might find it hard to entertain yourself while waiting.

Another option is to search for a ride to the airport, the Waze application allows for users to give rides for people for a fee, or look at FB groups if someone is available for a ride, but this isn't guaranteed, and wouldn't be something I would count on.