| There are actually two separate, but related issues here.
The first is the reference pitch used to tune your bass. Typically, the reference pitch is A440, meaning that the note A above middle C is exactly 440Hz. This simply means that when you play this note on your bass, regardless of which string you happen to use, it will sound at 440Hz. This ensures that the notes on your instrument will match the same notes played on other instruments tuned to A440.
In certain situations, a slightly different reference pitch may be desirable. For example, if you are accompanying a piano with A tuned to 400Hz, it's a lot easier to tune a bass than tune a piano, so you tune your bass down to match the piano. You should ask the musicians you play with what reference pitch they use for tuning to be sure you pick the right one. However, the vast majority of the time (in my experience playing rock), A440 is what you want.
The actual tuning of each of your strings is a separate question, and is the primary factor in determining how your bass should be setup. As others have mentioned, for a given set of strings, lower tuning mean less tension, and the neck and the bridge need to be set up accordingly. If you tune the lowest string on a 5 string to A, there will be less tension than if the same string is tuned to B. The setup will take this into account.
You should make sure the setup is done using the same gauge/brand strings you plan to use, as different strings may have different tensions with the same tuning.
I suggest you decide which tuning you play most often, and have the bass set up for that tuning. You can try other tunings with this setup and see how they work for you. If you need to use two or more very different tunings, you may want to have separate instruments, each set up for a particular tuning.
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