We can solve this problem by using a Venn diagram. Let's start by drawing two circles, one for Time and one for Newsweek:
```
_________
/ \
/ \
/_______________\
| |
| |
| |
| |
| |
| Time |
| |
| |
| |
| |
|_______________|
\ /
\ /
\_________/
Newsweek
```
Let x be the number of families that subscribe to both magazines. Then, we know that:
- 75 - x subscribe to Time only
- 50 - x subscribe to Newsweek only
- 5 subscribe to neither
We want to find the value of x. We know that the total number of families surveyed is 95, so:
Total = Time only + Newsweek only + Both + Neither
95 = (75 - x) + (50 - x) + x + 5
Simplifying the equation, we get:
95 = 130 - x
x = 35
Therefore, 35 families subscribe to both Time and Newsweek.