"I have slept with the mice."
Translation:Ik heb met de muizen geslapen.
Grammatically speaking, only 'Ik heb met de muizen geslapen' is correct. The past participle (voltooid deelwoord, in this case 'geslapen') should always be at the end of a sentence. They will absolutely understand you when using 'Ik heb geslapen met de muizen' as quite a few Dutch people make this mistake too, it is just not correct.
I don't know if the Flemish do this, I am Dutch myself but do not speak with Flemish people on a daily basis. The Dutch certainly do, I even doubted whether your answer was correct or not. 'Ik heb met de muizen geslapen' just sounded better to me than 'Ik heb geslapen met de muizen', and after a bit of research I found out that the first one is grammatically correct. Just being curious: are you Walloon or Flemish (as you are learning Dutch)?
The only Google hit for sleeping with mice: http://edukado2017-malawi.blogspot.com/2017/07/day-15-16-and-where-we-live.html