Yes you can press charges by making a report with the police, no way to tell if it will be a prosecutable case, but definitely make a report. At least to spare the next woman torment.
You can always make a report. However, the case is not very strong. The delayed report along with the lack of evidence (rape kit, you being able to testify first hand that it happened) makes it unlikely that he would be convicted. This is an honest answer based on my experience as a prosecutor and a defense lawyer.
Go to the police station that covers the area where it happened.
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Yes you may file a complaint with the precinct where the incident occurred as the statute of limitations on a rape case is at least five years. No one can state with certainty whether the police will make an arrest in a case with a 6 month delay in reporting and where it sounds like your only proof is a statement made by your ex but it's a pretty weak case in terms of evidence for a jury.
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Yes, you may report the rape as the statute of limitations has not run.
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