i5, and which 7850? the cheapest 7870 goes for 220, about the cost of the higher costing 7850. If anything get a 6300, itd compare more against the 3470, but in the situation using the bulldozer 6200 the i5 wins
Nowadays the cheapest ivybridge i5 is the i5-3350p, so you might want to check that cpu if you want an intel cpu, the 7870 is obviously better, if you can fit it with the i5 the better.
If not, you might take a look on the amd side with the FX-6300(not the 6200 which is from the older bulldozer architecture) and the 7870.
Another suggestion is to look for a 7870 tahiti le if the 7870 you had in mind is at the same price as of the 7870XT.
tahiti xt is the reg ular 7850/7870 codenames or something like that i believe the LE is the same thing with some defective parts so certain amounts of things are disabled, as for the lower cost, but still performs similar to the reg edition i think
Tahiti le means it's a different version, with a different gpu(tahiti), you can't crossfire the 7870 tahiti le/7870 XT with the normal 7870s(it has the pitcairn gpu), but with the 7900s series, since it uses the same gpu, amd got a poor branding name for it, it should be called a 7950 le or 7930, basically it's a somewhat crippled 7950, but it terms of performance much alike with the 7950 and it's better than any 7870.
In sum, a good buy if you can afford it. http://www.tomshardware.com/reviews/tahiti-le-7870-7930...