When phosphoric acid (H$_3$PO4) and calcium hydroxide (Ca(OH)$_2$) are mixed, a chemical reaction occurs, resulting in the formation of calcium phosphate compounds and water. The reaction can be represented as follows:

3H$_3$PO$_4$ + 5Ca(OH)$_2$ → Ca$_5$(PO$_4$)$_3$OH + 9H$_2$O

In this reaction, three moles of phosphoric acid react with five moles of calcium hydroxide to produce one mole of calcium hydroxyapatite [Ca$_5$(PO$_4$)$_3$OH], a type of calcium phosphate, along with nine moles of water.

Calcium phosphate compounds, particularly hydroxyapatite, are commonly found in biological systems and have significant applications in various fields, such as dentistry, medicine, and agriculture. In dentistry, for instance, hydroxyapatite is used as a primary component in bone grafts, dental cements, and toothpaste to promote teeth mineralization and strengthen tooth enamel.