I do both for the reasons you stated. The usual way of incorporating them would be to alternate between cycles, however there is another way that I used very effectively but it will complicate your increments.
I start a cycle with DB and progress them about twice as fast as the other exerciaes so that I’m completing the 5s by the end of the 3rd week and then start the 4th week switching over to BB and progress them to the end of the cycle. Doing this also helped because it was hard to increment DB throughout an entire cycle just because the top weight I could use was so low compared to BB.
Just a thought in case you want to give it a try.