The rupee today fell by 25 paise to trade at nearly five-week low of 44 rupees 79 paise against the US dollar in early trade.Dealers said dollar strength against the euro and a lower opening in the stock markets mainly put pressure on the rupee, which slumped to a five-week low.The rupee had closed 23 paise lower at a more than two-week low of 44 rupees 55 paise against the US currency in the previous session on sluggish local equities and dollar demand from importers.