Some constructions for 1-rotational BIBD's with block-size 5

We give miscellaneous constructions for 1-rotational (4q+1,5,\lambda)-BIBD's, being q an odd prime power, investigating their possible resolvability whenever q=1 (mod 10). Concerning Steiner 2-designs, the strongest result that we obtain is the explicit construction of a 1-rotational (4q+1,5,1)-BIBD (with a multiplier of order 5) for each prime q=1 (mod 30) such that ${11+5\sqrt{5}\over2}$ is not a cube (mod q). As a particular consequence of our constructions, we get new (125,5,1) and new (156,6,1) BIBD's. The only ones with these parameters previously known were those obtainable form the 3-dimensional affine and projective spaces over $Z_5$.