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."

Grimsby Town said it "fully supports the letter" issued by fan group the Mariners Trust to Stevenage FC.
The Mariners Trust made the allegations about the treatment of some fans after the two sides met on Saturday.
Stevenage FC said it implemented "a full, 100% compliant, searching regime" after fears of "the potential for anti-social and un-cooperative behaviour".
More on this and other Grimsby stories
In response, Grimsby Town said that after being contacted by the Hertfordshire club it reassured them "that risk issues would be minimal".
The club added: "It was suggested to Stevenage that positive engagement would result in a fun and issue-free day and that the only small risk they faced was a chance of smoke bombs from a small section of younger supporters aged 15-25, as this happened at Chesterfield."
"GTFC does not condone searching of minors (under 13s) or the questioning of females about the contents of their underwear."
The letter from the supporters' group alleged stewards asked some female fans "if they could feel their bras" if they told them they were were underwired.
It claimed the searches were "in full view of male stewards, fans and police" and described them as "a gross invasion of privacy".
The fans group also said children as young as five were subjected to full body searches and supporters had items confiscated that were not listed as being banned, such as "contact lens solution, cough sweets and medication".
Stevenage FC said the searches were implemented because "after liaising with Grimsby Town's safety officer, the police and others, it was indicated that prohibited items were likely to try to be brought into the grounds and could be passed onto those deemed less likely to be searched, such as women and younger supporters".
Grimsby Town said it would be raising the issue with Stevenage.
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.
[NEXT_CONCEPT]
A football club has criticised searches of its female supporters who were asked to show their bras to security staff.