Let the five numbers be ( x_1, x_2, x_3, x_4, x_5 ). The mean of these numbers is 39, so their total sum is ( 5 \times 39 = 195 ). When one number is excluded, the mean becomes 35 for the remaining four numbers, giving a total sum of ( 4 \times 35 = 140 ). Therefore, the excluded number is ( 195 - 140 = 55 ).
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