The problem that I have is that I always have a big spike (10-15 dB) directly on the center frequency of my V5 (no matter what frequency I set). The amplitude of this spike changes in dependency of the choosen span. How to get rid of this spike?

That spike is probably nothing surprising – just the LO leakage/DC offset, a very common artifact in direct conversion receivers!

The easiest solution is not to use Center Frequency (LO frequency) for your measurement but configure a little offset.