Final answer:
The priority nursing problem for a client diagnosed with dementia who is disoriented, wandering, has a decreased appetite, and is having trouble sleeping would be Risk for injury.
Step-by-step explanation:
The priority nursing problem for a client diagnosed with dementia who is disoriented, wandering, has a decreased appetite, and is having trouble sleeping would be Risk for injury. While the other options may also be valid nursing problems, the risk for injury takes precedence because the client's disorientation and wandering behavior could put them in immediate danger, such as falling or getting lost. Other nursing interventions will be needed to address the client's altered sleep pattern and imbalanced nutrition, but ensuring their safety and preventing injury should be the priority.