Setting the Render Range
What you need to do is to start your render 5 seconds into your animation. You can accomplish this by setting the start frame to 5 seconds worth of frames into your animation.
To determine how many frames are in 5 seconds of your animation, look at the Frame Rate setting in the Dimensions section of the Render tab:
Here we see that the animation's is set to have 25 frames per second (fps). So, to determine how many frames are in 5 seconds, simply multiply 25fps x 5 seconds = 125 frames.
Then, just set your Start Frame to 125:
Another way to specify the Start and End Frames for your animation are in the Timeline window:
For a detailed description of how to set the Start Frame and End Frame for your animation, see the answer here.
You can also read more about render output settings in the Blender Manual.