List at least five of the major controversies surrounding private-sector prison providers

The subject of privately built and operated prisons is among the most hotly debated, even polarized issues in the United States. There are many sources that can provide numerous items for your list. This answer provides some reasons and suggests sources to find others.
AFSCME, the union for federal, state, county, and municipal employees, is strongly opposed to privatizing these and other private services. Their reasons include low wages and unsafe working conditions; the latter is related to lack of safety overall in terms of workers' ability to keep prisoners in their cells.
The Sentencing Project, which works on criminal justice system reform, also has extensive materials about its opposition to private prisons. One major point they raise is that the widely touted cost savings are illusory, and largely arrived at by omitting some of the real costs.
https://www.afscme.org/now/why-prison-privatization-is-bad-a-case-study

https://www.sentencingproject.org/publications/capitalizing-on-mass-incarceration-u-s-growth-in-private-prisons/