TPS7A7300: Max recommended output is 5V, abs max is Vin+0.3V. What is the impact of an output of 5.3V?

Hi David,

Yes the TPS7A7300 should work with Vout=5.3V as the absolute maximum voltage with respect to ground for it and the input pin is 7V.  It is important to note that the electrical characteristics in the EC table will not be covered for these conditions since they are beyond the EC table conditions. That being said it is unlikely that there will be a big shift in performance for such a small change in the conditions.

Below are my answers to your specific questions

1. Absolute max for "out" says Vin+0.3. If our Vin is 5.7V, so we are ok (we are below 6V)? Yes Vin=5.7 is less than the recommended maximum of 6.5V so that is not an issue. 
2. In fact, I want to know if the only care about the difference between recommended 5V and abs max Vin+0.3 is the heat dissipation or there is something else to take into account? No, this abs max is not directly related to heat dissipation. If Vout goes above Vin+0.3V or 7V (which ever is lower) transistors can break down due to excessive voltage, or either metal lines or parasitic diodes could be damaged due to reverse current when Vout>Vin+0.3V
3. Does going a little bit higher than 5V can lead to a premature death of the part? 300mV should not much of an affect on the life time of a part. The biggest contributor to premature failures is temperature. So if that is a concern for this application make sure to connect the thermal pad to as much metal as possible as this is the most effective means to reduce the thermal resistance between the die and the ambient air. 

-Kyle