Resistors getting hot in this MOSFET driver circuit
Here is your circuit being discussed:



R3 and R5 should not be getting "hot".

Do the math.  Even if Q1 were a perfect switch, there would only be 5 V across R3.  (5 V)2(1 k&Omega;) = 25 mW.  Unless this is a very tiny resistor, you wouldn't normally notice it getting warm.  A 0805, for example, can usually dissipate about 150 mW safely in open air on a typical PCB.  This is &frac16; of that.

It should be obvious that R5 dissipates less power.  Even ignoring the B-E drops of Q3 and Q2, there is only 3.3 V across R5 when Q1 is off.  That results in 11 mW.  You're not going to feel that with a finger.

Therefore, something is not as your schematic shows.  Perhaps the 24 V is applied somewhere unintended.  Perhaps the resistors aren't the values you think they are.  1 k&Omega; resistors would be labeled "102" or "1001", depending on tolerance.

As an aside, this circuit has some questionable tradeoffs.  I can see how it may appear to work, but you can do better with about the same parts and topology.  However, that's not what you asked about.  For example, I wouldn't have been surprised if you said Q2 and Q3 were getting hot.  That would be expected due to the bad design.  But, any of the 1 k&Omega; resistors getting hot makes no sense for the circuit as you show it.