Opamp which works with 5 V input
Yes you can use a 741 opamp with a voltage at the inputs between -5 V and + 5 V as long as you give it a supply voltage of at least - 8 V and + 8 V (this is my guess, the 741 has a guaranteed +/- 12V input voltage range when a +/- 15 V supply is used, I re-used that 3 V margin (15 V - 12 V) to get to +/- 8 V) note that that is a symmetrical supply voltage, not a single 5V or 12 V supply.

You should read "Reasons not to use a 741 op-amp?" some alternatives are suggested there.

You can use an opamp with a single 5 V supply and have an input voltage of - 5 V, not at the input of the opamp but at the input of the circuit. The limitations of the opamp you use are related to limitations of the circuit design but they are not the same. 

For example, suppose I have an opamp which has a limited input voltage of for example 2 V to 3 V. With that opamp I can still design a circuit that can handle a 0 V  to 5 V input voltage. It only relies on how I use the opamp.

I also recommend you read "Opamps for everyone"

Some of the other answers here draw conclusions from the Maximum Ratings and the Recommended Operating Conditions. Actually these numbers are completely irrelevant. What is relevant is the Input voltage range, source: The TI datasheet.



Note how this is a table with Electrical Characteristics

The Input voltage range is specified to typically be +/- 13 V but it has a (guaranteed) minimum of +/- 12 V. In a commercial (mass produced) design you would use this +/- 12 V as that you can rely on. The +/- 13 V cannot be relied upon. Also very important: note (1) under the table, this lists the operating conditions which must be applied to get the values listed in the table. Important here is the +/- 15 V supply as the Input Voltage Range is very dependent on the supply voltage that is used.

Yep, reading (and understanding) a chip's specification isn't easy :-)