Answer:
 yes
Step-by-step explanation:
75000 is a 5-digit number, as are all the numbers up to 75000. 5 digits are sufficient to assign each student a unique number.
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Comment on the answer
Usually, at least one check digit would be used to guard against errors such as transposition of digits. Many school districts have a lifetime longer than 10 years, so it seems likely the number of students in 50 years (for example) will exceed the 100,000 students that can be given 5-digit numbers. A 7-digit numbering scheme seems more appropriate, or a scheme that uses a combination of digits and letters.
