Ahhh, good question. I am not a statistics guru, perhaps another member has more knowledge on this than I do.

I can tell you that in practice most people use statistical analysis software for this job. A good program will give you many different ways to analyze the data.

You see, you may want to look at different aspects of the data, for example how each component affects the result (for example "a" and "c" might be very influential) (I seem to recall Analysis of Variance is useful here, look for the term ANOVA or MANOVA)

But if you just want to do a simple job, put the data into Excel and play with it!

Oh, got it the wrong way around LOL!

OK, I need to know a little more. Is the data "soft" or "hard" (my words), in other words, is it

A) like a survey where the data is not exact, or
B) is each one an actual equation (ie, if you have values for a to e then they will always get the results shown)

If it is A) then it is Statistics, in other words something like "people who have 12 of a, and 26 of b ... have a satisfaction level of 9". And in Statistics there are many different ways of solving the "best fit", depending on how the data was collected and what results you want.

If it is B), then just pick any 5 and solve them, the rest should also be right

You should be able to reduce the number of equations, let's try an example:

a+b=2c
a-b=c

That has 3 unknowns but only 2 equations, so let's do our best to solve it:

Combine the two: a+b = 2c = 2(a-b)
Therefore: a+b = 2a - 2b
Subtract a from both sides: b=a-2b
Add 2b to both sides: 3b = a

So we end up reducing this to:

a = 3b

So, we have a range of solutions.

For example: b=1, a=3b=3, a+b=4, a-b=2, c=2
Or: b=2, a=3b=6, a+b=8, a-b=4, c=4
etc ...