2 × 5 (smallest rectangle)
7 × 15 (smallest odd rectangle)
complete
smallest rectangle: 2 × 5
smallest odd rectangle: 7 × 15
Klarner [1, Figure 11] originally gave the 7 × 15 rectangle.
Also see
Torsten Sillke's P pentomino page.
Reference
[1] David A. Klarner,
Packing a
Rectangle with Congruent N-ominoes,
Journal of Combinatorial Theory 7 (1969) pp. 107-115.
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Updated August 23, 2011.