Let x = the number of yellow flowers
Let y = the number of red flowers.
There are a total of 75 flowers, therefore
x + y = 75 (1)
For every 5 red flowers, there are 10 yellow flowers, therefore
x = 2y (2)
Substitute (2) into (1).
2y + y = 75
3y = 75
y = 25
x = 2*y = 50
Answer: 25 red flowers.