Yep! Sounds like a sucker to me....
I read on a website to......

Try and pull the sucker out rather than cutting it off. It helps to loosen the soil around where it emerges from the ground. They grow direct from the rootstock and pulling them off is thought the lessen the chances of another forming, whereas cutting it may promote more.

Nope, absolutely NOT necessarily a sucker, this is not a useful way to decide whether its a sucker. Some roses produce both 7 and 5 composite leaf formations, there is some variation. But there are more definitive ways to decide.

A sucker always arises from below the graft or scion, the lumpy bit at the bottom of the rose stems, just above the roots. This part, the graft, is often buried below ground, so If the stem you're worried about is coming from below ground, check its point of origin by scrabbling the soil away from it and checking if its above, or below the graft..

Other ways to tell are, the sucker shoot may be much more thorny, the thorns may be different, smaller and more numerous, than those on the rest of the plant. They also have a tendency to grow straight up and at a much faster rate than the non suckering shoots on the rose. They may also be a different colour - the stem might be paler, along with the leaves, compared with the rest of the plant.