The n-variable and m-resilient (m>n/2-2) Boolean functions achieving both the upper bound on nonlinearity2^n-1-2^m+1and the upper bound on algebraic degree n-m-1 must have three valued Walsh spectra: 0,±2^m+2,which are called saturated best (SB in short). Using the known results of weight distributions of the cosets of the (32,6) Reed-Muller code and a new construction method for SB functions gives the number of the 5-variable SB functions.