Suitable sampling rate for triangle wave
The 5kHz is the repetition frequency and it's not the maximum frequency of your signal or its bandwidth and your signal isn't band-limited but it has small frequency content over very high frequencies which lead to the Fat32 answer.

but there are other sampling and reconstruction scheme for non band-limited signals like Finite Rate of Innovation (FRI) which could perfectly reconstruct certain families of non band-limited signals like piecewise polynomials (which your signal exactly fits in) with finite sampling rate (in your case 6 sample per each repetition).