A small apartment, or a room is around 400 EUR warm if you have little claim to location and equipment. Find out more at immonet. de. The user interface is simple and even if you don't know German, you should be able to use it.
The cost of living for a geek who lives sparingly would be 400 EUR per month. Insurance and miscellaneous costs 150 EUR.
Leaves you with 5000 * 0,5 - 400 - 400 - 400 - 150 = 1550 EUR should be doable as a monthly saving. With a buffer, a monthly saving of 1400 EUR should be possible.
60000 EUR annual salary is ok for the beginning. If you perform well, you should earn a six-digit salary as a Senior Software Engineer, especially in Hamburg, Munich and Düsseldorf. To do this, however, you would have to set the right course at your first job in Germany and not start with less than 75,000.