I understand why you used it (how else could you concisely describe that beat pattern?), but I briefly thought your phrase "5-3-5 rhythm" referred to time signature, which caused some confusion, since thirteen beats to a measure seemed deeply unlikely.

Permit me some music geekery, and I'll explain how "5-3-5" could resemble a time signature. Most common signatures have a natural default for which beats are emphasized: a measure of four puts emphasis on the first and third beat, a measure of six on the first and fourth. But a measure of seven could put emphasis on either the first, third, and fifth beats, or the first, fourth, and sixth. Sometimes, to make it explicit which is desired, a composer or arranger will write in the time signature, instead of "7", "4+3" or "2+2+3" for the first, and "3+4" or "3+2+2" for the second. These are usually read aloud as "two-two-three" and "three-two-two", respectively.

Measures of three also have two variants, though it's never written into the time signature. Polka time goes "oom-pah-pah", treating the second and third beats of the measure identically. In waltz time, on the other hand, the pick-up (the last beat of the measure) is almost as important as the downbeat (the first), to such an extent that it would make sense to notate it as 2+1 rather than 3.

To write a suggestion of the "HTT rhythm" into the time signature, one would use 3+2+3. (6+4+6 would imply emphasis on notes that don't have it.)