Looking at the AMD site the 5570 does support eyefinity so getting 3 monitors to work is doable... unless you have some weirdo model.
I'm not sure why you have vga involved at all. Stick with digital connections and it should work.
FWIW, my 5870 has the same outputs as yours and monitors connect natively to each one.
#1: FX-6350, Antec Kuhler 920, MSI 970 Gaming, Powercolor R9 290X, ASUS Xonar D2X, GSkill (F3-14900cl9d-8gbxl), Antec Truepower New 750, Arc Midi, Win8.1pro x64
#2: MSI A88X-G45, AMD A10-7850K, Asus 5870v2, Antec900 case, AMD 2x4GB 2133 (R938G2130UK), Antec 750 True, 128GB Sandisk SSD, WD Black 1TB, Win8.1pro x64
#3: Athlon 64 X2 4200+, AGP 1950pro, Audigy 2, Asus A8V-D, 2gig ram, Enermax 465P. Now on Win8.1pro cat 10.2