The difficulty isn't in decoding, which is a problem Howard's excellent circuits handle fine. For accurate timing the problem is having a real time, low latency device capable of measuring the 'events' as they happen.

There are circuits in this thread which use a microcontroller to timestamp the data, these get good enough precision. Moving all decoding and timing to an FPGA (with averaging of multiple hits) gets both accuracy and precision even closer. Then there's the fancy analogue magic that AMB use (probably patented) that will get you the last bit of accuracy.

The Raspberry Pi is a great device but a normal operating system isn't going to get you accuracy or precision. You'll still need all of the decoding and timestamping to happen in a dedicated circuit.

Lastly many of the RTL SDR devices are designed as TV tuners (for DVB-T). These generally wont be able to tune low enough to get to 5Mhz-10Mhz. Even the HackRF (designed from the ground up as an SDR) isn't rated below 30Mhz.