In the NADP\(^+\)-malic enzyme type C\(_4\) photosynthesis cycle, the assimilation of one molecule of CO\(_2\) requires 5 molecules of ATP. This is because the cycle involves the carboxylation of phosphoenolpyruvate (PEP) and subsequent steps leading to the formation of malate, which is then decarboxylated to release CO\(_2\) for the Calvin cycle. Each turn of this cycle consumes ATP to regenerate PEP and support the carboxylation process.
Thus, the value of \(n\) is \( \boxed{5} \).