The significance of mosaic is that there is no gap after several figures are tiled, that is to say, a vertex of a certain figure can be filled 360 degrees.

For example, squares and regular triangles, the internal angle of squares is 90, and the internal angle of regular triangles is 60.

Suppose there are x squares and y equilateral triangles inlaid, then there are at some vertex.

90x+60y = 360 (both x and y must be positive integers).

The solution is x=2 and y=3. In other words, two squares and three equilateral triangles can form 360 at a certain vertex, so they can be inlaid.

The internal angle of a regular Pentagon is 108, and the internal angle of a regular triangle is 60.

If there are x regular pentagons and y regular triangles,

Then 108x+60y=360 can't find that X and Y are positive integers, so it can't be mosaic.