Your employment history in the past five years should show continuous employment, for one or several employers.
Having worked for one employer for four years, for example, would be 4 years of work history without gaps. To make this the necessary five years, you simply provide information showing you were also employed (by probably a different employer or employers, but potentially the same) for at least a year in total prior.
The purpose of such a screening criteria is to ensure you have not spent significant time out of the workforce within (what they consider to be) a reasonably recent period, and as an additional indicator of those who may not be reliable or committed employees.
The date on which you start a new job should ideally (for them) be the same as the date on which you end the previous one, for all starts and ends of jobs in the time period. However, it will not probably be an issue if gaps are rare, or are very short (i.e. less than two weeks).