My water comes out of every faucet in my house fine except for my outdoor spicket and washing machine (they are on the same line). When I turn the water on it might come on right away or it could take up to 5 minutes to start flowing.

Is there a stop valve on that line between where it branches off the main cold water line and the washer or outside faucet?

Yes for the outside faucet, but only at the washing machine for the other line.

I don't think I understand you response. You have a stop valve for the outside faucet, but is there another valve before the washer? That is, between the washer and where the line (1/2") branches off from the main cold water line which would be 3/4" probably. You said they are both on the same line, is that correct?

The problem with the washer was the internal screen. Now I just have a problem with the outdoor faucet.

Good.
The problem with the outside faucet can only be either that there is a loose washer or there is something blocking a valve. Either can occur in either the stop valve or the faucet. First turn off the stop valve then remove the valve stem from the outside faucet. Check the washer screw to make sure that the washer is tight. You may want to take the washer out and turn it over and use the other side for a while.
Open the stop valve and see what kind of flow you get. If you don't get a good flow try running a small wire back up the valve port to see if you can dislodge any thing blocking the valve.
If you have no success there turn off the water at the main valve and remove the valve stem of the stop valve. Check the washer there. If the washer looks OK there, replace the stop valve. Notice that I didn't advise running the wire back up the input port of the stop valve. You could do that an possible clear the blockage but what ever is blocking the valve is still there and will only come back to haunt you later.
What could be blocking the valve? Assuming copper pipe it is most likely a piece of solder from soldering the pipes together. A piece of solder can lay in a pipe for years moving and blocking a valve.

From what you have described I am inclined to believe that the problem is a blockage and that it is at the stop valve.