Due to computational bounds, most SVM-based phonotactic language recognition systems consider only low-order n-grams (up to n = 3), thus limiting the potential performance of this approach. The huge amount of n-grams for n ≥ 4 makes it computationally unfeasible even selecting the most frequent n-grams. In this paper, we demonstrate the feasibility and usefulness of using high-order n-grams for n = 4, 5, 6, 7 in SVM-based phonotactic language recognition, thanks to a dynamic n-gram selection algorithm. The most frequent n-grams are selected, but computational issues (those regarding memory requirements) are prevented, since counts are periodically updated and only those units with the highest counts are retained for subsequent processing. Systems were built by means of open software (Brno University of Technology phone decoders, HTK, LIBLINEAR and FoCal) and experiments were carried out on the NIST LRE2007