Abstract: 
The cell-like approximation theorem of R. D. Edwards characterizes the $n$-manifolds precisely as the resolvable ENR homology $n$-manifolds with the disjoint disks property for $5 \leq n < \infty $. Since no proof for the $n=5$ case has ever been published, we provide the missing details about the proof of the cell-like approximation theorem in dimension $5$.

1. Department of Mathematics
   University of Tennessee
   Knoxville, TN 37996-1300, U.S.A.
   
2. Department of Mathematics
   Brigham Young University
   Provo, UT 84602, U.S.A.