You have two basic problems.
First, if you "want the LED to be off until a high signal is applied to the gate", you need to use an NFET, not a PFET. Your PFET's turn on when the gate goes negative relative to the source. This is why the spec sheet's Product Summary gives a value for its on resistance (RDSon) when the gate-to-source voltage (Vgs) is at -10V (note the negative polarity, meaning the gate is at a lower voltage than the source).
The traditional way to turn off a switching FET is to bring its gate to the same voltage as its source. In your case, with the PFET's source connected to +12V, that would mean the gate would be at +12 too. Then, when you want the PFET to start conducting, you bring its gate to a lower voltage. How much lower? The spec sheet uses -10V in their product summary, which is a pretty strong clue! That would mean the gate would be pulled down to at least +12 - 10 =) 2V above ground in your circuit. And since the spec sheet also says the gate is good for +/-20V, you'd be just fine pulling it all the way down to ground which the gate would perceive as -12V relative to the source.
However, all of this means the LED would be off until a LOW signal is applied to the gate - the opposite of what you've stated as your goal. Helpfully, an NFET's gate polarity is just the opposite: It turns off when its gate is positive relative to its source. Hence why you really want an NFET to achieve the polarity you seek.
Your second problem, however, is an issue regardless of which type of FET you use. You say you "want to control the mosfet with a microcontroller at 5 volts", but you're running the FET from a 12V rail. To turn the FET fully on, or fully off, you need to swing its gate as far as possible (to ground, or to its source voltage). This means you need 1) a FET that specifically has a logic-level gate threshold voltage, or 2) a gate driver transistor to isolate your MCU's pin from the +12V that the gate resistor will expose it to, or 3) to drive the LED from the 5V rail used by your MCU.