So, in my case where it’s the basement temperature I’m fermenting at, would us-05 be a better yeast for me to use?
No, not if you are brewing a lager.
What is your basement temperature?
Is it colder in the winter/warmer in the summer? (mine stays about 40F in the winter, 60's in the spring and about 70 in the summer)
Keep an eye on the temps and brew lagers when its cold down there, Ales in the spring and maybe some Belgians in the summer.
I have a temperature controlled fermentation chamber, (freezer w/conrtol unit) but I still ferment lagers in the late winter/early spring using chilly ambient basement temps and then use the freezer for lagering.
If you have a furnace in the basement, it probably won't get as cold as mine does.
The answer for the original question is: It depends on how long it took your beer to get chilled down. The dry yeast doesn't start turning wort into beer right away, it takes a while to build up the yeast population and really get going.
So you might be ok, but it might not be the "cleanest" lager you've ever sampled.
It will still be beer.