Help! High noise with 5N at ISO 800

Hi, I am still quite new to photography so don't kill me, but I don't understand the high noise I get at some pictures. I understand that underexposure can create noise, but it is this the case here and is it normal to this extent?

If so, what can I do to create a reasonable looking picture without blowing out the background? If that's not the reason, what is/could be the problem?