Short answer: only if it was a misdemeanor (NOT felony), or if the records are closed or expunged. Click above title for more info:

To answer your question strictly as posed, of course a person can say they were never convicted of a crime even if the conviction was yesterday. The issue is, what are the consequences of lying on a job application? Beyond the moral question of honesty there is the question of being caught, and you will have to weigh the consequences of admitting and explaining your past legal issues versus denying and hoping for the best. Such philosophical issues are beyond the scope of library advice.

For information about Massachusetts' Criminal Offender Record Information system, and how it effects a job search, you can check out Mass Legal Help's page on Criminal records and Applying for Jobs. According to information on that page, the five-year limit would apply to misdemeanors only, not felony convictions. See this page.

The Massachusetts Trial Court Law Libraries has a rich site on the state law on criminal records. To take steps to legally seal a criminal record (at which point you can answer "no" about convictions), see especially this section.