The problem is that my latching relay has voltage rating of 5V (not 3V as in design), and rated coil power of 1W, and my GPIO pins of MCU can output only 3.3V (not 5V input as in design).
I do have a 5V VCC that comes from external power supply.
Is is possible to fit this design to 5V, 1W latching relay?
Your circuit will not interface (will not work) to a 3.3v microcontroller.
Here is a circuit for an "H-bridge" that will work on 5v and can be connected to a single output line of a microcontroller operating on a supply of 3.3v.
Simply connect the microcontroller to the base of Q3 and remove all the components from the front-end of the circuit.
I don't think so. First, your relay coil is only going to see about 3.5 volts, which may not be enough. Secondly, and worse, 3.0 from your MCU may not turn on the top Darlington pairs. It may work, but it's too close for comfort.
It's an open collector array. It doesn't drive outpours high plus it has the voltage drop problem. Why not use a dual coil latching. Very easy to drive.