Should I include the fee in the sent bitcoin amount? I'm using Electrum and want to purchase something with Bitcoins. When I get to the bitpay screen with all the details (And the timer) I input the information into the electrum client, which then generates a Fee for the transaction.

My question is: I need to send an exact amount, will the fee take the amount straight out of the amount being sent (And therefore send too low an amount) or do I need to add the fee to the amount being sent?

i.e Let's say the site requests exactly 0.05 bitcoins, fee is 0.02. Do I send 0.07 and let it take the fee, or do I send 0.05 and it takes the fee out of the wallet another way?

Thanks.
The fee is going to be separate from the amount. 

Using your exmaple:
If you need to send bitpay 0.05 btc, you enter 0.05 for the amount field and 0.02 for the fee field. Do not send bitpay 0.07 btc

If you specify a fee of 0.02 btc and you only have 0.06 btc combined in all of your addresses, electrum will alert you that you don't have enough. 

Please note that the fee is something that you decide you want to include. It is not a fixed value, but there is a minimum if you want to get your transaction included into a block in a reasonable amount of time. Looking at the current block, 402557, transaction fees look like they are around 0.001 btc. The fee can depend on a couple of things like age of coins, size of transaction, and/or how fast you want your transaction included. You may also want to increase the fee since more and more blocks are reaching the size limit and miners will favor a more profitable transaction.