The five were a 16-year-old girl, who died in Great Victoria Street on Monday, and four men who died in different parts of the city.
Police did not confirm which three cases are suspected to be drugs-related but no single, common drug is involved.
Earlier, a senior officer said all five deaths may have involved drugs.
But a Police Service of Northern Ireland (PSNI) spokeswoman later clarified that detectives suspect drug misuse may have been a factor in only three of the deaths.
Post-mortem examinations are being carried out and toxicology reports have been ordered.
The first of the five sudden deaths took place in Verner Street in Belfast city centre on Friday, 31 March.
The other four people, including the teenaged girl, all died on Monday:
Police said that number of deaths in such a short time frame was unusual, but that they were not linking any of them at present.
Ch Supt Tim Mairs said: "Investigations are at an early stage, but I would like to take the opportunity to reinforce the dangers posed by taking any illegal drugs or any medication that is not prescribed for you.
"Drugs misuse can affect anyone and we recognise that many vulnerable people are being exploited for the financial gain of those higher up the supply chain."
He added: "The number of deaths in Northern Ireland connected to drug use is on the increase and this is a concern.
"Sadly, these are all preventable. In fact, more people are dying from misuse of opioid drugs in Northern Ireland than in road fatalities, which is a very stark reality."
Five sudden deaths in greater Belfast over the past few days are being investigated, with police saying three of the cases may have involved drugs.