In short - yes you can upgrade it - all the processor variants on the g510 are 64bit.
The main problem is that although you have a 64bit processor, you've installed 32 bit Windows 7 and the windows 10 upgrade will only let you upgrade to 32bit windows 10.
If you are happy to do a clean install and you can back up all you important data then you can install 64bit Windows 10 - but don't forget - THIS WILL WIPE YOUR DISK!
If you have 3GB of memory or less, don't bother trying to upgrade to the 64 bit version as it generally needs a decent amount of memory to be happy.
Microsoft say 32bit win10 needs a minimum of 1GB and 64bit needs 2GB - These are bare minimums - they'll run, but will likely be subject to slowdowns if the OS uses the pagefile much I would probably have a minimum of 4GB and prefer 8GB for 64bit win10.
While digging around to make sure of my facts, I came across a guide if you really want to go for it.
The first sections about cpu and hardware shouldnt be a problem as it's a fairly recent laptop.
Anyway, here's the guide