Final answer:
The new nurse should first assess the newly admitted patient with acute flank pain and hematuria, as these symptoms suggest a rapidly-progressing condition that could become critical and require immediate medical intervention.
Step-by-step explanation:
Considering the patient scenarios presented, the new nurse should assess the patient with acute flank pain and hematuria first. This patient may have a condition such as a severe infection or kidney stones that could quickly become critical.
The symptoms indicated are suggestive of a rapidly-progressing pathology that may require immediate attention to prevent deterioration of the patient's condition. While urinary retention related to BPH and a patient who underwent a renal biopsy are also important to assess they do not typically present with symptoms as immediately life-threatening as those of the newly admitted patient. The patient scheduled for hemodialysis likely has established protocols and timing in place and would not be the top priority unless they are exhibiting signs of urgent complications.