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You need 7 days to cover whole of Leh and Ladakh. If you could plan for 10 days then you will be covering best spots too.
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Depends from where you start and which type of travel experience you want to take. People often take bike tours and start from manali and end it at srinagar (11-12 days starting from your city to returning), You can take flight and reach direct leh and then spend 5 days there, it will be enough (7 days complete tour). You can also ask friends who have already been there. Duration to explore Leh depends on the mode of transport.
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