They need to meet their audience where their audience can meet them. Just about every phone nowadays can access Twitter in an immediate and obvious way. Twitter will meet their audience where their audience needs to be met.
Hence, if their time constraint is 5min, fine by them, otherwise the question stands: what is their constraint.
And Twitter is not real time (this is obvious if you ever used it - it is more visible in the mobile version), there's no guarantee that if a tweet was sent by an account A in time T and the timeline of someone who follows A is opened some seconds later that tweet will show up.