How many axes of symmetry does a pentagon have?
No it does not.
An ordinary pentagon has none. It can have 1 or, if it is a regular pentagon, 5.
In general, a square. A square always has 4 lines of symmetry. A pentagon need not have any. Only a regular pentagon can have 5 lines of symmetry. But if you created pentagons from sides with random lengths then, assuming the pentagons existed, only a tiny fraction would be regular: most pentagons would have no axes of symmetry.
A general pentagon may have no symmetries at all. A regular pentagon has five symmetry axes - each one connecting a vertex with the middle of the edge opposite this vertex. A regular pentagon also has rotational symmetry - if you rotate it by any multiple of 72 degrees clockwise or anti-clockwise you get a regular pentagon as well. Please also see the related link below.
A regular pentagon has 5 lines of symmetry, running from each vertex to the midpoint of the opposite side. These lines are not to be confused with the five lines it takes to draw a pentagon. Every regular polygon has as many lines of symmetry as there are lines in the polygon. An irregular pentagon may have none or 1 line of symmetry.
A pentagon is a plane area which is enclosed by five straight lines. It is, therefore, a polygon. The sum of the five interior angles of a pentagon sum to 540 degrees and so, each interior angle of a regular pentagon measures 108 degrees. A pentagon has five diagonals. It can have none of five axes of symmetry.