Is it a digit haiku? We can read 13576870234289 digit-by-digit in English, and it makes a haiku:

one three five seven
six eight seven zero two
three four two eight nine

We say it's a &quot;digit haiku&quot;, because when read out like this, it's 5+7+5 syllables long, and no word is broken across a line.
For example, 111171111101111 is not a digit haiku, even though it has 17 syllables:

one one one one se-
-ven one one one one one ze-
-ro one one one one

Two-syllable digits (0 &quot;zero&quot; and 7 &quot;seven&quot;) are not allowed to span the 5th-and-6th syllable positions, or the 12th-and-13th syllable positions. (Other than that, any 17-syllable digit string makes a digit haiku.)
All other digits beside 0 and 7 are one syllable long in English.
Task
Given a non-empty string of digits (or list of numbers) 0 through 9, decide whether it forms a digit haiku.

You can assume the string does not start with 0, and thus you're also permitted to take input as a number.

You can assume the input is at most 17 digits long. However, it may be more than 17 syllables.

This is code-golf: aim to write the shortest answer, measured in bytes.


Test cases
7767677677 -&gt; True
13576870234289 -&gt; True
123456789012345 -&gt; True
11111111111111111 -&gt; True
9 -&gt; False
9876543210 -&gt; False
11171111101111 -&gt; False
111171111101111 -&gt; False
998765432101234 -&gt; False
77777777777777777 -&gt; False
Retina 0.8.2, 25 bytes
0|7
_#
^.{5}\w.{6}\w.{4}$

Try it online! Link includes test cases. Explanation:
0|7
_#

Expand 0 and 7 into two syllables.
^.{5}\w.{6}\w.{4}$

Check that neither the 6th nor the 13th syllable is the second such syllable.