Beggars belief how these original 'crossply' tyres have lasted this long?...even stood still in one spot!
Still, 5.60 is 5.6 inches and that is the tyres tread width, crossply tyres are as high as they are wide so tyre wall is also 5.6" making aspect ration 100% this then if you measure these tyres, the overall diameter should be 2x5.6+13, that equals 24.2 inches or 615mm
With modern Radial ply tyres the wall height is always less than 100% of the width, commonly 80% or less, so in your case to obtain the correct ride height for the van when it's sitting on it's new tyres you need to buy a wider tyre
Give or take, your original tyres 5.6in in metric are 145mm but radial are only 566mm diameter, 155R13 tyres are 578mm ,165R13 is 596mm and 175R13 = 610mm diameter.
It would then seem 175R13 is ideal BUT, is the rim wide enough to take them? and if they do fit the rim, is there any clearance problem inside the wheel arch?
Any decent tyre fitter will be able to tell you what will and will not fit your rims. However I doubt 175's will while I'd expect you'd be unlucky if the 165R13 don't fit? this size being a pretty good compromise only dropping the van by about 10mm or 3/8in
Next problem then, can the chosen tyre size carry the weight of the van? probable answer to that is yes so that leaves finding a suitable pressure to run them at?