never really had trouble interfacing 5V TTL and 5V CMOS components together. In some speed critical and over a hughe temparature range operating mixed devices ther might be some problems.
what should a pullup be used for??
The 74HCT means "High Speed Cmos TTL", the component it self is a CMOS device with the driving capability as a TTL component (10 devices).
So in fact you are interfacing two cmos devices. no problem....