This problem provides a rich context for visualisation and suggests
many similar lines of enquiry.
For example :

Can all letters of the alphabet be represented using only a 5 by
5 array of cubes ?

Is it possible to create every combination of three
letters in a 'perforated cube' ?

What difference does the orientation of the letters make ?

How many ways are there to orientate three nonsymmetric letters
such as F, J and P ?

What difference will it make to use letters that have symmetry
of some kind ?
For any chosen combination of letters and orientation, explore
the variation possible in successful arrangements.
 Can every solution arrangement have either more cubes added or
some removed, and still be a solution arrangement ?
 Is there a relationship between the maximum and minimum number
of cubes for any solution ?
Exploring the perforated cube problem, and related questions, using
cliptogether plastic cubes will provide invaluable 'concrete'
sensory experience for students as they stretch their powers of
visualisation, express the problem, test their conjectures, or
represent their solutions.
The Freudenthal Institute for Science and Mathematics Education has
some very useful Java interactivities.
Follow this link to access these environments :
www.fi.uu.nl/rekenweb/en/
The best interactivity for this problem is called '
Building Houses ', but 'Building free '
and also 'Building Houses with Side Views ' are both excellent
resources for problems of this kind. As always, Java can take a few
seconds to load.
In 'Building free ' you need to type 5 into the size box if you
want to match the context of this Perforated Cube problem.
The information above is repeated on the
Hint page which also contain this
excellent
video of one
solution for E, S and H 
video of
an ESH solution