How many Amps can I pull through the USB to the 5V pin?

The short answer is 500mA sustained. You can pull up to 1A for short periods of time before the reverse back-feed diode starts to overheat and could be damaged. Anything over 1A will likely kill the diode very quickly.

This is not just about the diode protection though. The PCB traces and plated holes have current limits too. Additionally, devices connected to the 5V pin can create voltage spikes and inrush currents that could damage the board or your computer's USB port.

Rather than trying to power current-hungry peripherals and LED strips through USB, you should power your current hungry peripherals and LEDs from an external 5V power source and also power your board from that source via the 5V pin.

For more details about the 5V pin's functionality, see What voltage range can the 5V pin accept and is it an input and output?