In theory, this is a problem solvable using the curvefitting toolbox, or lsqnonlin (optimization TB), lsqcurvefit(optimization TB), nlinfit(stats TB),etc. So it depends on what toolboxes you have available, although each of those tools has a somewhat similar calling structure. You could also use fminsearch to do the optimization if you have no more than about two terms in the sum, since fminsearch tends to be poor for large problems in general.
In practice, sums of exponentials problems quickly become impossible for more than a couple of exponential terms. You need to have great data, with very low noise. Lots of data is good too, as long as it is low noise. Even then, you will ABSOLUTELY need good starting estimates for the parameters.
The problem is this quickly becomes highly ill-posed. Any noise at all will blow it out of the water, yielding garbage for results. If you think you can solve this with n=5 or so, you are just wasting your time.