Final answer:
The Catholic Church reached its height of power during the High Middle Ages, particularly in the 11th century with the investiture controversy when the Papacy gained authority over church appointments. Its political and spiritual influence was considerable by 1500 but started to decline with the Protestant Reformation in the early 16th century.
Step-by-step explanation:
The Church reached its height of power in the period just before and during the High Middle Ages, which began after AD 1000. A significant turning point was during the 11th century, particularly with the investiture controversy. The Catholic Church, also known at the time as the Latin Church, under the leadership of the pope, gained substantial control over the appointment of church officials through the prohibition of simony - the buying of ecclesiastical privileges - by Pope Gregory VII. This culminated in the excommunication of Holy Roman Emperor Henry IV and a subsequent rebellion against him, showcasing the papal power.
By the year 1500, the Church had established itself not only as a spiritual authority but also as a significant political force within Western Europe, holding sway over monarchs and influencing the direction of states. Its power began to wane with the onset of the Protestant Reformation in the early 16th century, as figures like Martin Luther challenged the Church's practices and authority, leading to a split in European Christianity.