Refer to this document
The Unix epoch and timestamps
milliseconds that have elapsed since midnight on January 1, 1970, UTC.
This date and time is called the Unix epoch, which is the predominant
base value for computer-recorded date and time values.
Note: It's important to keep in mind that the date and time is stored
in the local time zone, and that the basic methods to fetch the date
and time or its components all work in the local time zone as well.
You can use this online datetime converter to check the date and time.
1569301200000-0500 is not Unix epoch but only
1569301200000 is, and it converts to below:
Datetime.newInstance( Long.valueOf( '1569301200000' ) ) returns 2019-09-24 05:00:00
0500 is just indicating that its 5am in GMT or else
-0500 could be time correction to get local time for which you can use DateTime.addHours or DateTime.addMinutes. In any case you need to get clarification from the webservice developers regarding what is 0500