Here is one Pentominous puzzle.

It is, in a sense, unique: it is the only 5 by 7 Pentominous puzzle that has two clues, an asymmetric unique solution, and a symmetric layout. More precisely, a layout with either central symmetry or axial symmetry about the longer axis is impossible, and, as to symmetry about the shorter axis, the only specimen is the one above.

There are, however, centrally symmetric Pentominous puzzles with two clues on a 5 by 5 grid (Here is one of them, and the other is obtained by replacing the N with a U) and on a 5 by 6 one (Nf5-Za1, Ff4-Wa2, and Td5-Wc1; the FW puzzle does not actually make use of the no-touch rule).

The following puzzle is somewhat unique as well: it is the only asymmetric-unique-solution puzzle with this layout.