This provides a path to +V.
The 10K pulls up the PNP base. When the NPN is off (its base = 0V) then the PNP is biased off. When the NPN turns on, its collector brings the PNP base to Gnd which turns it on and the 5000? determines the PNP's IB.
That's a lot of IB, actually, playing rough that. I used 1K in my verification. Try higher values, 2K - 5K, for starts. You will have to play with that value, depending on your PNP hFE and your LED strip current demand. I don't have that info.
Experiment with that using a couple of regular LEDs in series with a 1K to Gnd, just to be sure you have it right. Get out the voltmeter, too.
(formatting)
--> Using a 2N3906, with a 5K you could probably pull 100mA [guesstimating].
Rev'd the dwg. I didn't want to take a lot of heat for suggesting to way over-driving the base. OK.