I looked for pictures and the only examples of a Steven's Peerless bolt action repeater I could find were based on a Steven's Model 66 and not a Savage Model 5. If the magazine tube moves with the bolt it's a Steven's 66 action - and I do not have an example to look at - from your description of what's happening it sounds like it might be a Model 5 action - either way I think the firing pin should retract for loading, in fact it almost has to in a 66 action because the cartridges are pushed straight up the front of the bolt face.

No matter which action it might be check to see if the firing pin can be easily pushed flush with the bolt face and will stay there with the bolt open. If it does that, then you might have a broken or missing firing pin return spring, or the firing pin could be broken so the nose of it does not get pulled back.