During the years 1903-1914，Ramanujan recorded most of his mathematical dis-coveries without proofs in notebooks.Although many of his results had already becn published by others，most had not.Almost a decade after Ramanujan's death in 1920，G.N.Watson and B.M.Wilson began to edit Ramanujan's notebooks，but，despite devoting over ten years to this project，they never completed their task.An uncdited photostat edition of the notebooks was published by the Tata Institute of Fundamental Research in Bombay in 1957.This book is the fifth and final volume devoted to the editing of Ramanujan's notebooks.PartsⅠ-Ⅲ，published，respectively，in 1985，1989，and 1991，contain accounts of Cbapters 1-21 in the second notebook，a revised enlarged edition of the first.Part IV，published in 1994，contains results from the 100 unorganized pages in the second notebook and the 33 unorganhed pages comprising the third notebook.Also examined in Part Ⅳ are the 16 organized chapters in the first notebook，which contain very little that is not found in the second notebook.In this fifth volume，we examine the remaining contents from the 133 unorganzed pages in the second and third notebooks，and the cIEums in the 198 unorganized pages of the first notebook that cannot be found in the succeeding notebooks.In contrast to the organzed portion of the first notebook，the unorganized material in the first notebook contains several results，particularly about class invariants，singular moduli，and values of theta-functions，which are not recorded in the second and tlurd notebooks.As in the first four volumes，either proofs are provided for claims not previously established in the literature，or citations are given for results already proved in the literature.
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