1: London, UK to Moscow, Russia (1,820 miles)
2: Kathmandu, Nepal to Bangkok, Thailand (2,130 miles)
3: Mexico City, Mexico to the Panama Canal (2,015 miles)
4: Melbourne, Australia to Perth, Australia (2, 135 miles)
5: Algiers, Algeria to Cairo, Egypt (2,033 miles)
Please note: Shorter in this case means shorter by available roads, which may possibly be in quite poor condition and so actual travel time is not calculated.
Honorable mention in this contest goes to the driving route for Baghdad, Iraq to Cairo, Egypt which while only 800 miles apart, will take over 4,000 miles to drive due to closed borders in the Middle East, which requires the driver to pass through Sicily on the way.
Source: Google Maps Driving Directions