\(\begin{array}{l}
y = {x^2} + 2\left( {m - 1} \right)x + {\left( {m - 1} \right)^2} - {\left( {m - 1} \right)^2} + 3m - 5\\
= {\left( {x + m - 1} \right)^2} - {m^2} + 5m - 6\\
GTNN\,cua\,\,y\,la\,\, - {m^2} + 5m - 6\\
Ta\,co:\\
- {m^2} + 5m - 6 = - \frac{{49}}{4} - {\left( {m - \frac{5}{2}} \right)^2} \le - \frac{{49}}{4}\\
GTLN\,la\,\, - \frac{{49}}{4}
\end{array}\)