How can Zakat be paid on money whose amounts were not recorded over five years, during which it accumulated for the purpose of marriage and was [subsequently] used for that purpose, knowing that the saved money reached the nisab and a full year has passed over it?

You are obligated to pay Zakat (definition) for the past years in which your wealth reached the nisab (definition) (threshold) and a full hawl (lunar year) passed on it, because Zakat is not forfeited by the passage of time. You must now estimate your wealth for each year and strive to pay the Zakat that will absolve your responsibility before Allah. You are not burdened beyond your capacity, for Allah Almighty says: ﴿Allah does not burden a soul beyond its capacity.﴾