The p does mean this one is silver? It weighs the same as the other nickels. Does it sopose to weigh the same or more? 4.9 grams.
Yup, that's 35% silver. Nice find! All 5c nickels are supposed to weigh about five grams, even silver war "nickels." Worth about a buck.
So far, you have found both major composition changes of US coins during WWII in circulation: the 1943 (zinc-coated steel) cent, and the 1942-1945 (56% copper, 35% silver, and 9% manganese) five cent pieces. Nice. Did you find the "nickel" roll hunting or in change?
All of the 43, 44 and 45's are silver. (Large MM over dome.) 42 made both kinds, 42, and 42-D regular, 42-P and 42-S silver (large MM).