This is never going to work unless you have been running 5.3 previously and have saved your SHSH blobs for firmware 5.3 (which I’m guessing you haven’t because if you had you wouldn;t bother downgrading to 5.0.2)
5.3 is now an outdated firmware, so it’s no longer being ‘signed’ by Apple. In order to install this firmware you would need to sign the firmware yourself using SHSH blobs. But you can only have SHSH blobs for firmware 5.3 if your ATV2 has been running 5.3 and you created a backup of your SHSH blobs whilst running 5.3.
You can only install a jailbroken firmware for which you already have SHSH blobs, or which is currently being signed by Apple. However the latest software for the ATV2 currently cannot be jailbroken, which is v6.2.1 according to the firmware wiki. Since 6.2.1 cannot be jailbroken your only option for running jailbroken firmware is to run a version that you have SHSH blobs for.
For instance, if you bought a old ATV2 off someone and it turned out to be running 5.3 you could backup your SHSH blobs, then use Seas0npass to jailbreak 5.3, sign it with the SHSH blobs and then reinstall the jailbroken version of 5.3 on your ATV2.
Since your device is on 5.0.2 all you can do is backup your SHSH blobs for 5.0.2 and then use Seasonpass to jailbreak and sign 5.0.2, and re-install the jailbroken version of 5.0.2 on your ATV2.
I’ve had my ATV2 for a while and have backup SHSH blobs for a variety of firmware versions along the way, so this enables me to reinstall any of these older firmware versions.