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.
cori check
You can check here: cori ma and see that there is a way to seal a record.
When a record is sealed it means that people outside the criminal justice system cannot see it. The police and the courts can still see it, but for almost everyone else it is like the charge does not exist.
Some Massachusetts criminal records can be sealed. If they are sealed, most employers will not be able to see them when they do a CORI check.
Btw- You do not have to tell employers about criminal records that have been sealed!
If it has been 10 years since all of your misdemeanor convictions have closed and 15 years since all of your felony convictions have closed, then your criminal record is eligible for sealing.
I also found this one when i searched for cori check it has a series of posts about cori massachusetts, employer's questions etc.