This is a somewhat complex assignment. The way you approach it will need to be based on your own experience in the field. An IT manager within the health care industry will need different skills and fill a different role than a nursing supervisor and an office manager in a small private practice will need different skills than a CEO of a hospital chain. As this assignment asks you to cover a fair range of topics, your first task might be to organize it.
You might introduce your paper with a paragraph about what you think makes a great leader. There is no right or wrong answer to this, as there are many different successful leadership styles. Some leaders are visionaries who lead by imagining a compelling idea of the future of health care while others are best at hiring and motivating skilled employees and supporting their visions. Some managers are very detail focused and others better at the big picture. Thus your first paragraph should focus on what you think is the most successful management style and one you most wish to emulate.
Your second paragraph might briefly describe your current responsibilities and the position you would like to have five years from now. After describing that briefly, you should show how the leadership style you most admire would help you be effective in that position. Address the types of expertise and daily supervisory skills you need (such as the ability to allocate staffing resources) and think about how you can go beyond just effective logistics to inspire and develop your staff.
As you work on this, you should take into account what sort of leadership style is most effective for what sort of staff. If you supervise highly trained experts such as doctors, you will be focused more on fostering their own creativity and expertise, but if you are supervising food preparation and delivery within a hospital, you may want a more authoritarian style, focusing on following strict protocols.