There is no connection between your Q5 and your laptop for email...none. Your Q5 is connected to your email server, as is your laptop (somehow, you don't say how...webmail? Outlook? Something else?). Depending on your email server and your configuration settings, your Q5 should be placing all emails you send from it into your server Sent Items folder. Depending on your laptop configuration, you should be able to see what your server Sent Items folder shows.
I wish I could be more specific, but not knowing your configuration (email service type, laptop email configuration, etc.), it's a bit difficult to give any more detail.
In "the old days", the method was to auto-CC or auto-BCC yourself on everything you send. Since newer technologies have come into existence, the ability of the device to place items you send into your Sent Items folder on the server has negated the need to do that, and that function no longer exists with BB10.
Occam's Razor nearly always applies when troubleshooting technology issues!
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