Strange. They're links to Home Depot here in Canada. Should be able to work?
Perhaps HD are blocking us because we are in the UK.
Edit: See comment above
And as far as the walls, this is a 1940s apartment building construction. And I'm in Montreal, Canada.
I have no idea what they were using in Canada 80 years ago. There have been some all concrete buildings erected here, such as those built from pre-cast panels made from the infamous "no fines" concrete - which incidentally are a pain to fix into, but mass concrete isn't that common in domestic work over here. Another problem in that our sizes are all metric, notvall the products are the same, and the terminology is a little different, too.
So the nearest size to 7mm is 9/32in and in the UK nylon (plastic) plugs to fit 7mm holes are generally called "brown plugs" because most manufacturers colour code plugs (red = 5.5mm, brown = 7mm, and so on). The nearest to a 5mm screw is a #10, as stated above, although a 6mm screw (equivalent to a #12) will also fit.
If the plugs you are referring to are Fischer DuoPower plugs:
then they will do the job, even if the wall material is a bit soft or crumbly. I'd still go for the longer screws, 70mm or 2-3/4 to 3in, because they t3nd to wedge themselves in better than shorter screws to resist pull-out
A note about concrete types: if the concrete you are drilling into is heavy structural grade or is of "no fines" type (a lot or large stones in the aggregate with minimal sand or small stone), you will need an SDS drill to make your holes because those types of concrete are so hard