I have a SNAPPER series 5. It will start but has no power and runs very rough. I have replaced spark plug, gas and air filter. I have also replaced the carborator, drained and added new gas. Drained and added new oil.
When the work was completed mower ran fine for about an hour, then it stalled and the ever since has been acting as mentioned above. Not sure of next steps. Suggestions?

First, put in a known good spark plug, preferably a Champion or NAME BRAND.
 
Second, next to the red on/off switch is a small squarish part.  It's a low oil switch.
If it detects low oil, it'll kill spark.  They do go bad...  Un-plug it and see if it helps. 
It won't hurt anything.  YOU just have to keep an eye on the oil level.  
 
Advise back..
 
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Hi there. The plug is brand new (champion).
Not sure what you mean by off/on switch. The mower starts with a key. I am not able to locate the low oil switch.

Can you advise what type mower this is? (rider, walk behind, zero turn, etc)
 
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Snapper series 4,5,6

There should be a model # on the ENGINE itself.  Please post that..
 
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2812523BVE

That #'s showing the entire mower, not the engine specifically:
 
https://www.ereplacementparts.com/snapper-2812523bve-7085622-125-rear-engine-rider-series-parts-c-207777_207778_208141.html 
 
There should be a model # on the engine itself..
 
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2199070131E1

Much better..
 
Your engine, an approx 18 HP Brigs, OHV engine: 
https://www.partstree.com/models/219907-0131-e1-briggs-stratton-vertical-engine/ 
 
I would check valve clearances first, make sure their not too tight..
https://outdoorpowerinfo.com/engine_specs/briggs_valve_gaps.asp 
 
Check and see if the spark plug is too wet.  I know you changed the carb but the NIKKIs 
are known to flood...
 
If all the above is ok, within spec, you'll need to do a leak down test.
If the engine was over heated, it can blow a head gasket and/or drop 
a valve seat..
 
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