The grid is 5x5, so any shape's dimensions must respect this. An area 6 shape like 1x6 or 6x1 is immediately impossible. Thus, the Orange 6 (at (0,0)) and Yellow 6 (at (3,1)) must be 2x3 or 3x2 rectangles.

The "Teal Square" (at (2,4)) is a strong starting point. In a 5x5 grid, a square containing cell (2,4) can only be a 2x2. A 3x3 square would extend beyond the grid boundaries. This forces the Teal shape to occupy (2,3)-(3,4).

Red 2 (at (1,4)): With Teal occupying (2,3)-(3,4), the cell (1,4) is on the rightmost edge, directly above the Teal 2x2. To be an area 2 rectangle, Red must be a 1x2 horizontal strip, occupying (1,3)-(1,4).

This clue is in the bottom-right corner. It's an area 5 rectangle, so it's either 1x5 or 5x1. If it's a 5x1 vertical strip, it would occupy the entire last column (0,4)-(4,4). However, this would conflict with our deduced placements for Red (1x2 at (1,3)-(1,4)) and Teal (2x2 at (2,3)-(3,4)), as they both need cells in column 4.

Therefore, the Brown 5 must be a 1x5 horizontal strip, occupying the entire bottom row (4,0)-(4,4).

This leads to a problem. If Brown 5 is the entire bottom row (4,0)-(4,4), it would occupy cell (4,3). However, we also have a "Green Bar" clue at (4,3). A distinct Green Bar cannot exist if the entire bottom row is taken by Brown 5. This important conflict highlights that these initial clues, if interpreted as distinct, non-overlapping rectangles, create an unresolvable situation within a 5x5 grid under standard Patches rules.