Answer
1,321,368,961
Work Step by Step
Number of strings of five ASCII characters containing the '@' at least once = Total number of strings of five ASCII characters - number of strings of five ASCII characters containing no '@' sign
Total number of strings of five ASCII characters = $128\times128\times128\times128\times128 = 128^5$
[5 decisions each with 128 options]
Number of strings of five ASCII characters containing no '@' sign = $127\times127\times127\times127\times127 = 127^5$ [[5 decisions each with 127 option, we can't use '@']
Therefore, answer = $128^5 - 127^5$ = 1,321,368,961
