Yes. Finishing all five questions counts toward your daily streak, whatever your score. You get one attempt a day, so a hard day is still worth finishing.
Answering all five questions extends your daily streak, even if you get none of them right. Leaving part-way does not count, because the day is not finished.
You get one attempt per day. Your attempt is saved in this browser, so you can come back to a half-finished day on the same device (where your result is kept). For more, read the Daily Five tips.