Pythagorean quintuple is a quintuple of five numbers a,b,c,d and e corresponding to the equation a^2 + b^2 + c^2 + d^2 = e^2. In the first part of the research, several different parametrizations of natural Pythagorean quintuples were discovered. Using the parameter selection, a Pythagorean quintuple is obtained, so the generator of Pythagorean pentacles is also called parametrization. The generator that generates all Pythagorean pentacles was discovered and also proved.In the second part of the research, in the set of the whole Pythagorean quintuple the multiplication was defined. It was proved that there is a multiplication unit, and that the multiplication is associative but not commutative. The dismantling of Pythagorean quintuples was also explored.