Thanks for clarifying my incorrect description of the LMA.
Actually, typing speed exceeded brain speed there. It's a quadratic approximation to the Chi square function, not the objective function (obviously perhaps, when thinking about it, since the algorithms look for the minimum of the Chi square function).
Another thought on finding the best set of five parameters. For a small total number of parameters (as in this case) an exhaustive search will work, and is guaranteed to find the optimal solution. For a large ttoal number it will be prohibitively slow though. A good approach then would be simulated annealing. Back in the days of MC11 that was available as a built-in function if you had the Numerical Recipes function pack, but unfortunately it's not available since then 
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