Does 5.1and above surround system have to have separate subwoofer ?

My current system is old dolby prologic system (2 tower, 1 center and 2 surround speakers) I would like to upgrade my receiver to newer surround system. Can I set the newer surround system (like 7.1) without dedicated subwoofer ? Can 7.1 system use only 5 speakers ? thanks
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