five-sided polygons cannot tessellate
You cannot tessellate convex polygons with 7 or more sides.
Mostly true - you cannot tessellate only regular pentagons in two dimensions, since you cannot sum up the intersection of the angles to 360 degrees. If you tessellate a regular pentagon in three dimensions, you end up with a dodecahedron.
A regular octagon will not tessellate - the 'spaces' left over are squares.
Most regular polygons will not tessellate but if their interior angles is a factor of 360 degrees then they will tessellate or if their angles around a point add up to 360 degrees then they also will tessellate.
Some can, but not all. For example, rhombi, rhomboids, oblongs, and isosceles triangles can tessellate; however, most irregular polygons cannot. * * * * * True, but an incomplete answer. All triangles and quadrilaterals, whether regular or irregular, will tessellate. No regular pentagon will tessellate but (as of 2016), there are 15 irregular pentagons which will tessellate. There are 3 convex hexagons, (regular and 2 irregular) which will tessellate. No polygon with 7 or more sides, even if it is regular, will tessellate.