Translation:I want a house with several bathrooms.
Swedish tends to differentiate more concretely in a number of cases that English finds words to be interchangeable.
As I understand it, 'flera' means more than one, while 'många' means significantly more than one. English kind of uses 'several' and 'many' this way in some cases, but not as strictly as Swedish does.
In this case, it's not likely that you would be misunderstood, but in some other cases, that distinction can be very important.
The understanding of colloqial, but standard forms of spoken English is woeful here. Anywhere in England / NI / Scotland 'would like' would be accepted here. ie in a restaurant " What do you want for a starter?" can politely be answered " I would like ... " meaning "I want"