I've seen varying times for spacecraft/rockets getting into LEO, e.g. according do the Mercury-Atlas 7 Wikipedia article, it took just over 5 minutes to get into a 259x154km orbit, whereas the Saturn V article says that it took a "typical" Saturn V launch nearly 12 minutes to get into orbit.
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2Around 10 minutes depending on the type of rocket, its load (manned flights tend to be slower to limit acceleration to survivable values) and the intended orbit, 5 min is extremely fast. – Hobbes Nov 24 '16 at 13:49
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1Hobbes is correct; 10-12 minutes is a typical time to orbit. Mercury-Atlas was an outlier as a result of its ICBM heritage; some modern launchers (e.g Ariane) use a very fuel-efficient, low-thrust upper stage which leads to a longer time to orbital insertion, up to 15-20 minutes. – Russell Borogove Nov 25 '16 at 02:25