As the person who introduced the concept of batched partitioned nonlinear least squares here, I'll assume you are asking about using my BATCHPLEAS utility, found on the file exchange.
Yes, in theory, you can use it to solve problems with any number of parameters. Of course, theory and practice need not always coincide. There is no limit (implicit or explicit) on the number of parameters you can estimate.
But first, are you talking about a problem with 5 NONLINEAR parameters, thus really more variables that that? Or as is common in this arena, if you have 5 total variables, then you might have 2 or 3 nonlinear parameters to estimate, but the remainder linear, so 5 total parameters? Remember that the partitioning reduces the search space for the estimation.
If you have no clue as to what partitioned nonlinear least squares is, or how it works, and the docs provided with BATCHPLEAS and/or FMINSPLEAS do not help you enough, then one of the chapters in the Seber & Wild book on nonlinear regression do cover the concept. And since Bates & Watts were the people who wrote the original papers on the topic as I recall, I'd bet that the book by Bates & Watts on nonlinear regression does so too. I think Seber and Wild called the idea something like separable nonlinear least squares.
Next, remember that regardless of how many nonlinear parameters there are in your problem, that nonlinear regression is often sensitive to starting values. BATCHPLEAS presumes the SAME set of starting values will be used for every member of the set. Problems with many nonlinear parameters might have local solutions that are not the global optimum. Or in some cases, some sub-problems might diverge, again due to sensitivity to the starting values. The more variables you have, the more risk there is in this happening. If partitioning does reduce the search space, so that in reality, you have only 2 or 3 unknowns, then the partitioning typically also increases the robustness of the problem, so it is less sensitive to the need for good starting values.
