Connecting Old Speakers to New Receiver

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Hey guys, for the past year or so I've been watching movies with wireless surround sound with the Sony DAV-HDX576WF.

I'm seriously considering buying a Pioneer Receiver to replace the Sony Unit. Here's my question:

Will I be able to use the 5 speakers and Subwoofer that came with my original system and connect them to the new Pioneer receiver? If so, is it difficult to connect speakers to a receiver that is not its own brand and use new wire to extend the speaker wire?

Thanks for your help guys.