As near as I can figure, you sent 5 BTC directly to a deposit address at an exchange (possibly Bitstamp)... It didn't go anywhere near your Electrum wallet. I suspect you may have "swept" the funds directly to the exchange.
For the record, that was the same day (15th August 2015) that the Bitcoin XT fork happened and the Bitcoin price was "only" ~USD$260... (10 days later it was $214, according to this:
https://99bitcoins.com/price-chart-history/ )
Does any of this trigger any memory? Perhaps you were cashing out before the fork?

Back then, your 5 coins were maybe $1250-1300... about 1/5th of what the 1.6BTC is worth now!

Anyway, what you do with the 1.6BTC you have left is up to you... Do you want to cash it out or keep it? If you want to cash out then just sweep the funds into a new wallet of your choice.
If you want to keep it, maybe you should consider moving to a new wallet as well, given the lack of faith in the current private key... If you didn't send the 5BTC then it may have been compromised.