The rupee fell by 5 paise to 62.36 per dollar in morning trade today at the Interbank Foreign Exchange market on increased demand for the US currency from oil importers. Increased demand from oil importers for the American currency also influenced the rupee, but a higher opening in the stock market capped the losses.The rupee had lost 15 paise to close at a five-week low of 62.31 against the dollar in yesterday's trade.Meanwhile, the benchmark BSE Sensex recovered by 75.73 points, or 0.36 per cent, to 20,863.03.