tricky issue.
is this your board?
http://www.asus.com/Motherboards/F2A55M_LE/#overview
it has 1x pcie gen 2.0 x16 slot running at x16 and another one at x4. so technically, you can crossfire two radeon hd 7850 cards. you need two of the same series e.g. 2x 7850 or 1x 7850 with 1x 7870 to crossfire. a 7950 can't crossfire with a 78xx card. you will need a crossfire bridge to connect the cards externally.
however, there are some issues. the bandwidth of the second slot is one-fourth of the first one, so it'll create problems in demanding gaming situations. another issue is that the x4 pcie lanes in the second slot is supplied from the fch(a55 chipset), no mention of possible disabling of i/o ports if the bottom x16 slot is occupied. another one is that your motherboard is microatx. 2x dual slot gfx cards on a microatx board is generally not advised, since a dual slot card ocupying the bottom pcie x16 slot blocks access to the bottom headers and ports.
now, to the parts you didn't mentions: case and power supply. the case needs to be able to support 2x cards. if the bottom is blocked somehow, it will block airflow to the cards.
power supply needs to be good enough to run 2x radeon 7850s and supply continuous power to every component.
lastly, the cpu. if it's running at stock clockrate, it will bottleneck the 2x 7850. moreover, your motherboard does not seem overclocking friendly, not that i'd recommend overclocking to a pc newbie. the apu platform is generally not suitable for 2x high end gaming cards.
to summarize: yes, you can crossfire. but it has lots of downsides for your configuration. in my opinion, you'd be better off buying a powerful single card like R9 290 or R9 280X (or radeon hd 7970 ghz edition), replacing the existing card.