As an answer to your PM...
For the first question, you just want P(Total 10 And <5 on red).
The text doesn't say "the probability to get 10 IF the red dice <5". It's "get 10 with red < 5"
The only possibility is red dice=4 and black dice=6, so it's 1/36, since you have :
P(Total 10 And <5 on red)=P(Red dice=4)*P(Black dice=6)