The tin with the serial tag is gone from your engine but it looks to be a model "5S"
I am unsure of the correct engine but believe it should be a slightly larger model, possibly a model "8"
I do believe it was made by Simplicity but the tires look to be Wards Riverside. That is why I believe it is a Wards tractor. I don't see any breakouts in the sidewall of the tires. IF thats the case the tires will be fine. If they won't hold air, patch the tubes or install new tubes and they will be fine.
IF YOU DO NOT OR ARE UNABLE TO PATCH YOUR OWN TUBES, TAKE IT TO A TIRE SHOP MAKE DARN SURE THEY KNOW NOT TO PUT 20 -30 LBS IN THE TIRES!!!. THREE OR FOUR POUNDS WILL BE FINE. Just enough to hold the tractor up. I know a guy that took an old walk behind wheel and tire to WalMart for a new tube and after the install they pumped it up to about 25 LBS before it blew. He HAD a really nice matched pair of tires for that tractor until that. The guy that blew the tire to oblivion said... "That tire must have been rotten" Those tires were not designed for more than a couple pounds of air and now that they are old they could be ruined easily. Those knobbie tires are very cool and seldom seen anymore so save them if you can!
This site has a moderator [Lauber1] that is very knowledgeable about those walk behind models and when he comes across this thread I'm sure he will be able to give you more info than I am able to do.
Best of Luck!!!