I have 5 more brothers than sisters, and each of my brothers have 3 more brothers than sisters. (If there are 10 family members total, how many are brothers)

I do believe that this problem should be edited to read: I have 5 more brothers than sisters, and each of my brothers
have 3 more brothers than sisters. (If there are 10 family members siblings total, how many are  brothers) MALES)

Let the number of brothers be B
Then number of sisters = B - 5
Including the NARRATOR, we get the following TOTAL-SIBLINGS equation: 1 + B + B - 5 = 10
                                                                             2B - 4 = 10
                                                                                 2B = 14
                                                          Number of brothers, or 
SCENARIO #1 (MALE NARRATOR)
Now, if a MALE narrator, the number of MALE SIBLINGS = 7 + 1 = 8. This gives us a total of 8 brothers
and 2 sisters, which means that each brother would have 7 brothers and 2 sisters, or 5 more brothers
than sisters. This makes the statement: "each of my brothers have 3 more brothers than sisters," FALSE.  

SCENARIO #2 (FEMALE NARRATOR)
Now, if the NARRATOR were FEMALE, and with the established number of brothers being 7 (see above), the number of
FEMALE SIBLINGS would be 3 (2 + narrator). This gives us a total of 7 brothers and 3 sisters, which means that the
narrator (one of the sisters) has 7 brothers and 2 sisters, or 5 more brothers that sisters. This makes the statement:
"I have 5 more brothers than sisters," TRUE. 

This also means that each brother would have 6 brothers and 3 sisters, or 3 more brothers than sisters, which also 
makes the statement: "each of my brothers have 3 more brothers than sisters," a TRUE one.

Hence, the NARRATOR is FEMALE, and there are 3 FEMALE and 7 MALE SIBLINGS!