let

x = the cost of the pen

y = the cost of the pencil

A pen and a pencil together cost $5.10

x + y = 5.10

The pen costs $5.00 more than the pencil

x = 5 + y

by solving the system of equations

x + y = 5.10

x = 5 + y

we find

x = $5.05

y = $0.05

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

the pen costs $5.05.

the pencil costs $0.05 or 5 cents.