Is there a shutter life in dslr cameras?

Some people say that there's a number of photos that you can take then the shutter will be broken
if there's
how many for the nikon d5000

Yes there's but the numbers for the major brands, Canon and Nikon can run up to about a million.
Most of Canon and Nikon's dslr cameras are rated at 100, 000 before even needing a tune up.
I have a friend, who contributes to this forum, who has a shutter count of a million with never a problem.

Bottom line, you'll want to upgrade long before a dslr will wear out.

Camera manufacturers run tests to see how long before their shutters wear out, in reality your shutter life will depend on other factors such as range of exposure settings used, type of mode (single shot etc)
just use your camera and if it wears out get a quote for a repair, budget models have a notional life of 50'000 exposures, pro models typically 150'000.

Play it by ear, it may wear under sooner, may wear out later, or more likely, you'll be onto a new camera before it's ever an issue.

The D5000 is specced for 100000 shutter actuations. Doesn't mean it will fail by 100001, does not mean yours will make it that far, just means that Nikon tested until they had a shutter that they felt would stand up to that number of pictures for almost all of the D5000s that would be produced.

On the next generation it's 150000 by the way