I don't know if that wallet is still online after this time but perhaps it was mtgox or blockchain.info? They are old and although you might not recognize the user interference as it was changed from years back you might remember the name.
2005 to 2007? i think bitcoin was just a twinkle in satoshis eye back then
Bitcoin is an open source peer-to-peer electronic money and payment network introduced in 2009 by pseudonymous developer "Satoshi Nakamoto"