Q:

How can I amplify PIR output to 5V

I need help with a project. I want to make a circuit to work as a night-time motion detector circuit that will power several LEDs. I bought:

1 LDR
some NPN transistors BC547 and 2N3904
some resistors 100kOhm
boost regulator 3V to 5V
PIR sensor

I connected the LDR to 2 NPN BC547 transistors and successfully tested it.
Then I connected the (-) from NPN transistor to the (-) of the PIR and the (+) of the PIR to (+) and the output of the PIR to a single led. It worked but the LED had a low output.
If I connect the PIR output to a 2N3904 transistor and after to the LED, the LED is brighter. But when I connect the current to the voltage booster and to all LEDs, the light is very low.
The problem is the 3.3V from the PIR output. I need 5V to work my LEDs. How can I establish this?
Update:
This is my PIR Sensor (mod edit: Pretty much a standard BISS0001 Design, no transistor on the output.)

My Power Supply Is 2 Batteries 3.7V 18650

A:

A boost regulator is not useful here. The problem is that your module, based on the BISS0001 PIR IC, the output pin is VCC (3.3v) 10mA max. Connecting a boost regulator to this output would be really limited.
All you need is a single transistor.

simulate this circuit – Schematic created using CircuitLab
Problem is that you need a transistor that works on the current provided from the output pin. Normally you see a 1k or 2.2k resistor on the board from Pin 2 of the BISS00001 to the output pin, which means only 2ma or 1.2ma at the output pin.
So you need either 1) a Transistor with a HIGH HFE or 2) a Darlington Pair (Two transistors in a pair).

simulate this circuit
These numbers are all based on the transistor you choose. A 2n3904 is only 100mA to 200mA max, with a hfe of 30 (So it multiples the base current, 1mA by 30, and that's the maximum current you get at the collector, 30mA).
You need to know how much current your led box needs, and what voltage it can use. I also assumed that your two batteries are in series.
See this page http://www.electrobob.com/fun-with-leds/ for a project that does both LDR and PIR for leds (but not the same way as what I think you want).
Adding the LDR as a night time detector is simple, and also requires a transistor.

simulate this circuit
Q1 and Q3 can be any weak small signal transistor (2n3904 100mA), Q2 should be a better one depending on your led box current needs (2n2222 1Amp). Adjust R2 for sensitivity.

