It definitely
can work. I had an Early 2009 (5,2) that I had 8GB in shortly while testing it just to see before giving it to my cousin with 4GB (800MHz too).
It was identical to yours. Early 2009 MacBook 5,2. 128GB SanDisk Ultra SSD, I had 10.6.8 and 10.10 on there, but eventually settled with Yosemite since my cousin likes the new look and features despite lack of TRIM support.
I had 2 4GB DDR2 sticks in it, 800MHz I think, but could have been 667. Both work in this model since the chipset supports it.
The sticks went elsewhere and are long gone now, but they were working fine for me. There are some screenshots out there from those who did the upgrade and had it working.
Image
Image
There is still a chance that it won't work, but it also should.
My Late 2008 MacBook (5,1) didn't work with 8GB out of the box, but through updates it did, it was an
EFI update with the system ROM of MB51.007D.B03 combined with 10.6.6 and up back then. It's had 8GB in it since 2011 and no issues for 3 almost 4 years.
So feel free to try it. Might as well. If it doesn't work return the sticks and go back to what you've got. Or upgrade all together if you really
NEED it (and have the $$$ of course).