let

x = the cost of one orange

y = the cost of one lemon

5x + 3y = we need to find the cost of five oranges and three lemons

Two oranges and five lemons cost $2.95:

2x + 5y = 2.95

Three oranges and two lemons cost $2.50:

3x + 2y = 2.50

by solving the system of equations:

2x + 5y = 2.95

3x + 2y = 2.50

we find:

x = $0.6

y = $0.35

click here to see the step by step solution of the system of equations:

5x + 3y = 5*0.6 + 3*0.35 = $4.05

five oranges and three lemons cost $4.05.