Drawing a RegionPlot from a Table of Values

ListContourPlot[matrix, Contours -> (Union[Flatten@matrix] - 1/2), 
 ContourShading -> None, ScalingFunctions -> {None, "Reverse"}]

Update: " a way to make the lines on the contour plot show the step shape as in the real table":

contours = ComponentMeasurements[matrix, "Contours"];

Graphics[Values @ contours]

ArrayPlot[matrix, ColorFunction -> "Rainbow", 
 Epilog -> {Thick, Values @ ComponentMeasurements[matrix, "Contours"]}, 
 FrameTicks -> All]

Edit

matrix = Array[RandomChoice[Range[5]] &, {10, 10}]; Table[
 RegionPlot[RegionUnion[Rectangle /@ Position[matrix, i]], 
  PlotPoints -> 180, BoundaryStyle -> None, 
  PlotStyle -> RandomColor[]], {i, 1, 5}]

Or

matrix = Array[RandomChoice[Range[5]] &, {10, 10}];
Table[Graphics[{EdgeForm[Blue], FaceForm[RandomColor[]], 
   Rectangle /@ Position[matrix, i]}], {i, 1, 5}]

Original

Representation a matrix as a colored square shape

Maybe like this.

matrix = Array[RandomChoice[Range[5]] &, {10, 10}];
position1 = Position[matrix, 1];
position2 = Position[matrix, 2];
position3 = Position[matrix, 3];
position4 = Position[matrix, 4];
position5 = Position[matrix, 5];
background = {None, None, 
   Join[Rule[#, Green] & /@ position1, Rule[#, Orange] & /@ position2,
     Rule[#, Cyan] & /@ position3, Rule[#, Yellow] & /@ position4, 
    Rule[#, White] & /@ position5]};
itemstyle = {Automatic, Automatic};
Grid[matrix, Frame -> All, Background -> background, 
 ItemStyle -> itemstyle]