Slice and Merge
Just use array_slice and array_merge like this:
$starttime = '5';
$endtime = '17';
$timings = array_merge(
array_slice($timings, 0, intval($starttime)),
array_slice($timings, intval($endtime) + 1)
);
Splice
Another way which is simpler and a (insignificantly) more efficient is using array_splice. Notice that it returns the extracted array, and changes the original array, so don't place the result inside $timings.
$starttime = '5';
$endtime = '17';
array_splice($timings,
intval($starttime),
(intval($endtime) - intval($starttime))
);