I got periods on 5th may last time.after that spotting occured on 18th.and my next period got on 13th june.is it normal to have 7 days delay ?

Several causes: The spotting that you had on the 18th was probably due to ovulation, since it occurred 13 days after the start of the may 5th menses. I agree that your menses is slightly late, by a week. It is not uncommon for women to have variations in their menses. Weight loss, stress, travel, illness, change in birth control, and new medications can all cause changes in the menses.