Can Shimano Tiagra 9 speed levers (ST-4500) be used with 105 brakes (BR-5700)?
As long as you use a Shimano brake caliper designed for a road STI lever, which is any Tiagra, 105, Ultegra, or Dura-Ace, they will work not just well, but perfectly. There may be a performance difference, but there will not be a compatibility difference.

Even most 3rd party brake calipers will work just fine.



New additional information: Starting with the Dura-Ace 9000 and Ultegra 6800 groups, there are differences in the brake caliper design which require levers which match the design. They also recommend, but do not require, a specific type of cable to get full benefit from the new brake design.