We establish that the necessary conditions for the existence of Bhaskar Rao designs of block size five are : i). λ(v - 1) ≡ 0 (mod 4) ii). λv(v - 1) ≡ 0 (mod 40) iii). 2|λ. We show these conditions are sufficient: for λ = 4 if v > 215, with 10 smaller possible exceptions and one definite exception at v = 5; for λ = 10 if v > 445, with 11 smaller possible exceptions, and one definite exception at v = 5; and for λ = 20, with the possible exception of v = 32; we also give a few results for other values of λ.