cable,
There are 3 different cartridges based on the same or similar cases and this can be a little confusing, but there is no reason to get spooked over them. First was the 22 Winchester Center Fire, a black powder 22 caliber cartridge. Then the Germans adopted it , loaded it with smokeless powder and a jacketed bullet at a higher velocity; and named it 5.6x35R Vierling( it was used in the small caliber barrel of many 4 barrel guns). The third is the 22 hornet which was also developed from the 22WCF case , and loaded to even higher velocity than the Vierling, necessitating higher pressures. Because of the higher pressures, the rim on the Hornet was thickened to prevent use in older, weaker rifles. The Germans call it 22 Hornet, usually, but when written in the metric system, it is 5.6x36R Hornet. The markings on your rifle, indicate it was chambered for 5.6x35R Vierling( 5.4 is the bore[not groove or bullet] diameter, and the 35 is the case length, the "R" is not shown because it is obvious from the extractor). If it will close on a 22 Hornet cartridge, then the rim recess has been deepened ( a good many have been). You have a very nice and fun combination gun that would have been used as a Schoenzeitgewehr to control predators during the "off season" when game animals are having and raising young. You don't need to make a chamber cast, just see it will close easily, or bind on a Hornet case. You should also "slug" the bore since they often used smaller than .224" bullets( smaller bullets are available). I happen to have a sxs combination gun in 24 ga. and 5.6x35R Vierling. After adjusting rim thickness on 50 cases and ordering .223" bullets, I am able to load cartridges using my existing 22 Hornet loading dies and shell holder. I load it to about 2350 fps and have an awful lot of fun with it. Your gun would be the same, except you can find 28 ga. cheaper than 24 ga. and it will be easier to have a scope mounted on it. You are very lucky to have found it- enjoy.
Mike