Hiding Five Colors

Is it possible to place five each of five colored coins in a 5x5 grid, such that each coin cannot "see" any other coins with the same color? Assume there are 4 inches between each grid point and each coin is 1 inch in diameter. Coins can be "seen" along ANY line of sight, unless another coin is in the way.

For example, red coins in the top-left and top-right corners cannot see each other because there are three other coins directly between them. However, a green coin in the top-left corner could see a green coin anywhere in the second row, since nothing is between them.

Source: Original.

Solutions were received from Brian Willett, Denis Borris, Claudio Baiocchi, Alan O'Donnell, Hagen von Eitzen, Jeremny Galvagni, Paul Botham, and Dave Peck. The problem is not solvable. Paul Botham's summary is a good example: 
Label grid squares A,B.. as below and 
consider placing a red (say) coin at I

ABCDE
FGHIJ
KLMNO
PQRST
UVWXY

Then the 4 other red coins may only occupy
some combination of positions F,G,Q,S,U,X

specifically:

(only one of F or G) + 
(only one of Q or U) + 
(only one of S or X)

but then only a total of 4 red 
coins can be legally placed
Alan O'Donnell's generalization is also a good one: 
Each of the 5 coins of any colour must all be on 'odd' or all on 'even'
points.
Sum of x,y coordinates = odd or even.
All odds can see all evens that aren't on the same row/column, and v-v.
As there are 12 odd and 13 even points, the 5th set of coins cannot be
placed.

Therefore, I believe this is not possible to do :-)


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