I installed new carb. on my tecumseh 5hp. snow king and it wont start. I have spark and gas is flowing out of carb.

This can be very frustrating and tough on the back and arm.
Always confirm the the fuel tank valve is open and the stop/run switch is in run position

It takes three things to run:

1. Compression. This is the resistance that you feel as you crank the engine. Some engines have compression release to assist getting the rotation started. You should be able to feel the compression stroke as you rotate, Remove the plug and you can easily tell the deference. If it had, last time used, been running and starting with no problem I would assume that the compression is OK. Gauges are available to check. at lease 120 PSI
2. Spark. It is near impossible to lose the spark timing on these. It can only be magnitude and presence. If in doubt about the condition of spark plug replace. I usually lay the plug on top of the head with wire attached and observe for the spark. No spark no start.
3. Confirm that the throttle is in the wide open position. It is possible during the repair the spring or rod has closed the throttle air valve. Air/fuel mixture is always hard to trouble shoot. I use open choke and starter fluid to conform that compression and spark are working. After that I will choke on a cold motor and pull listening for the first fire. At the first fire I would usually half choke and pull to first run. Full choke for many pulls will only flood engine!! If no joy then I would allow engine to vent and go back to start fluid. If it will run on start fluid than either carburetor is messed up or quality of fuel is bad.