3.3V signals to a shift register IC with a 5V supply
It is not guaranteed to work. You could use a level converter chip xx145, or you could use a 74HCT595, which will accept valid TTL levels at the inputs (and a 3.3V CMOS chip will give you that). 

Edit: The margins are fine for 3.3V input, as alexan_e mentioned. See below. 



Note that you should not connect any outputs form the HC595 or HCT595 directly to the 3.3V circuit. 

A simple single-transistor level shifter was discussed here:

If you use a MOSFET you don't need the base resistor, so it can be even simpler.