Catalysis of the reaction: 1,5-bisdiphospho-1D-myo-inositol 2,3,4,6-tetrakisphosphate + H2O = 5-diphospho-1D-myo-inositol 1,2,3,4,6-pentakisphosphate + phosphate + H+.
inositol 1,5-bispyrophosphate 2,3,4,6-tetrakisphosphate 1-pyrophosphatase activity