["09.10.2017", "10.10.2017", "11.10.2017", "12.10.2017", "13.10.2017"]
<select class="table__select" onclick="sendAjax()"></select>
const select = document.querySelector('.table__select');
// или
const [ select ] = document.getElementsByClassName('table__select');
select.innerHTML = arr.map(n => `<option>${n}</option>`).join('');
// или
select.append(...arr.map(n => new Option(n)));
// или
for (const n of arr) {
const option = document.createElement('option');
option.text = n;
select.appendChild(option);
}