DOE help needed: how to design an orthogonal array of 5 factors each with 5 levels

[#1]

I tried the Screening Design in JMP 12 and used discrete numbericals for these five factors. With 5 levels, it gives me the minimum 21 experiments.

I want all experiments to the orthogonal as possible. 21 experiments are too many.  Is there a way to use factional factorial design in JMPs to reduce the number of experiments? 

[#2]

A design for five discrete numeric factors each of which has five levels means that you will have an intercept and the first-order term through fourth-order term for every factor so the minimum number of runs is 1 + 5(4) = 21.

If you use a custom design instead the minimum number of runs is the intercept and first-order term for every factor so 1 + 5 = 6. I would not recommend the minimum number. A 12-run design is likely to find a few very large first-order effects but the design will fail if many of these effects are not null.

Do you really expect X*X*X and X*X*X*X effects in the response?

Could you define a wide factor range for each of the five factors (produce a large effect) and include X*X to cover non-linear response? That would require five continuous factors in a custom design with minimum of 11 runs.

[#3]

To add a bit to my colleague @Mark_Bailey's reply, I too suggest the JMP Custom Design platform. First a question for you?

Is your experimental goal screening? Optimization/characterization?

This answer will lead to different selections within the platform as you set up the design.

Nevertheless;

Use the model effects window to articulate the effects of interest...and this is where Mark's advice comes into play. Enter only the effects that are really needed. Then you can use the Number of Runs "user specified" to fit your run constraints. Then the effects will be as uncorrelated as possible given the factor levels, model specified, and # of runs. Take a look at the color map of correlations within the Design Evaluation subplatform to get an idea of the effect correlations for the design and power for your desired effects. Lastly, you can use the Compare Designs platform to compare design alternatives as well.