I'm looking for examples of this repeating pattern as a bass. Not these specific notes, but what is it called when you have five notes played quickly and many times?
The general term for a repeating bass figure is ostinato. It is rare to see a bass line moving in steady sixteenth notes, but it is very common to see bass lines moving at steady pulses in other notes values: wholes notes, half notes, quarter notes, and eighth notes. You mention that the notes are played quickly, so I'll focus on the last two notes values.
A steady bass line made up of quarter notes is often called a walking bass line. This is common is jazz, but it does not usually feature repeating phrases of five notes. Instead, walking bass lines in jazz tend to be less predicable.
A steady eighth note bass line is a characteristic of boogie woogie. One of the most characteristic boogie woogie bass lines closely matches the contour of your example.
As a bass-line, this specific pattern doesn't have a special name. However, there are some terms that apply.
- pentachord or pentascale: a five-note scale
a pentachord may be any consecutive five-note section of a diatonic scale. (Wikipedia)
- ostinato: a repeating motif
In music, an ostinato [ostiˈnaːto] (derived from Italian: stubborn, compare English, from Latin: 'obstinate') is a motif or phrase that persistently repeats in the same musical voice, frequently in the same pitch. (Wikipedia)