The 34,35Al b decays have been studied at the CERN online mass separator ISOLDE by b-g, b-g-g, and b-n-g measurements in order to corroborate the low-level description of 34Si and to obtain the first information on the level structure of the N521 isotope 35Si. Earlier observed g lines in 34Al decay were confirmed and new g transitions following both b decay and b-delayed neutron emission have been established. The first level scheme of 35Si includes three excited states at 910, 974, and 2168 keV. Indication is found for Jp 5(3/2)2 and (3/2)1 for the first two excited states, respectively. Beta-decay half-life of T1/2538.6(4) ms and b-delayed neutron branching value Pn541(13)% were measured unambiguously. The significance of the single-particle energy determination at N521, Z514 for assessing the effective interaction in sd-f p shellmodel calculations is discussed and illustrated by predictions for different neutron-rich isotopes.