Generally we're not using 5% strenght, we're using the strength at 5% strain. The reason is based on the strain compatability of the system. Since a granular soil will fail at 5% strain, that's also the mobilization limit for the geosynthetic. It makes some sense since most geosynthetics reach their peak strength at something around 11% strain, the increase in strength between 5 and 11% can only be mobilized post soil failure.
Some recent strain based methods, K-stiffness for example, are promoting using the secant modulus at 2-3% strain.