The picture of my house is at least five years old. When will a new picture be taken?

If you are referring to satellite images that are owned by Pictometry International Corp that are referenced through MicroSoft's website, you should probably ask them.  But it is not 5 years, it is closer to 1 to 3 years.  That is just how long it takes the satellites to pass over the same location again.

Some private satellite companies are doing better now.  Both Microsoft and Google are getting aerial images from numerous providers.  Zillow provides access to both Google Images and Microsoft images.  Zillow has no images of their own other than what you upload as an owner (or your agent).

Goggle's street views are never used for the main image on a home-details page.  But for those images, it just depends on how often Google's vehicles drive specific streets.  Many small rural streets have not been driven by Google's photo vehicles at all.  Some larger city streets in more dense areas with more changes have been driven as much as twice a year.

Just remember, that 10 years ago, if you wanted a satellite photo over the internet, you paid $10 for it, it was black on white, the pixel size was 3 feet across, and it was taken by a Russian Satellite.  Commercial Satellite photos on the internet have changed a lot since then, but still you are not going to get anywhere close to "real time" any time in the near future.

(Also remember that the satellite photo image companies have to filter out the images that have lots of cloud cover, as those just are not useful to most people, so this can create extra delays in some areas with substantial rain, fog and snow).

The picture will be updated as soon as you take one and upload it.
Here is a link to the Zillow FAQ tab that has answers to a number of similar questions.
Just under the property description is an Edit menu.  In the Edit menu is an opportunity to upload the photos.