At least 5 people died in Bangladesh and more than 200 are injured.
At least 5 persons died in Bangladesh and more than 200 are injured.
You could probably have answered this with a quick Google. This dictionary explains the historic difference.
Historically, "persons" was used to describe a specific, countable number of individuals. So in your examples above, "persons" would have been the correct word to use, because they have been counted, and there are 5 of them.
"People" was once therefore only used to describe an undetermined number. However, that is no longer the case, and the dictionary link I gave above explains that for several decades "people" has been preferred as the plural of "person" in all uses. "Persons" is not incorrect, but tends to be used only in extremely formal settings such as legal documents.
Persons can be archaic and not. If not, then it is only used in official, law language or to highlight how those 'persons' are respected.
Persons under the age of 18 are not allowed to buy alcoholic drinks.
Police must have a legal reason to arrest persons who are accused of having committed a crime.
You see, it's an official law language. These sentences would be acceptable in a law book in a certain context.
Example of highlighting how the persons are respected:
The new apartment building will have wheelchair access for persons with disabilities.
Otherwise it's just archaic and you should avoid it.