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In such question of distribution which involves identical objects to different boxes , the solution is nothing but similar to number of non negative integral solutions of the equations.In this case it will be :

x1 + x2 + x3 = 5  so  n = 3 , r = 5 ..So

No of ways of distribution  =  No of non negative solutions

                                       =  n-1+rCr

                                       =  3-1+5C5

                                       =  7C5

                                       =  21

Hence 21 is the number of ways of distribution..

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