No, you shouldn’t do this. Without an ORDER BY clause you shouldn’t rely on the order of the results being the same from query to query. It might work nicely during testing but the order is indeterminate and could break later. Use an order by.
SELECT * FROM table1 ORDER BY id LIMIT 5
By the way, another way of getting the last 3 rows is to reverse the order and select the first three rows:
SELECT * FROM table1 ORDER BY id DESC LIMIT 3
This will always work even if the number of rows in the result set isn’t always 8.