How to drop 6 volts to 5 volts
The actual voltage available from 4 x AA alkaline cells would vary widely, between 6 Volts for fresh batteries with no load, to as little as 0.7 x 4 = 2.8 Volts under load or as the batteries deplete. The voltage could fall further, but it is convenient to select 3 Volts as a lower operating limit.  

For a requirement such as described, one solution is a SEPIC converter that will produce the nominal 5 Volts desired, despite the supply voltage changing from greater than 5 Volts to less.

Most SEPIC converters these days appear to be available solely as SMD parts, which the question precludes. Therefore, an alternative solution is to use a pre-built SEPIC module that can be plugged into a breadboard. For example, this module on eBay (US $6.85 with free shipping) offers to 0.5-30 Volt adjustable output, from a 3-15 Volt input supply:



Searching your preferred vendor site would yield many other such options. 

Note, though, that realistically the battery voltage will drop significantly the moment the motors are turned on: AA cells have a significant internal resistance, which causes this voltage drop. The options are to use a LiPo / LiFePo4 battery instead, or use lithium non-rechargeable (primary) high current cells. 

The SEPIC module above will work with those as well.

It is also worth verifying whether the H-bridge / motor actually requires 6 Volts to operate: If this is a hard limit, then 4 x AA will not be viable anyway, so see the above alternatives.