Use the Symbolic Math Toolbox:
syms T x r k K_c
Eq1 = T==300+200*x
Eq2 = -r==0.1*k*(1-x-(x/K_c))
Eq3 = 2500==x/(-r)
Eq4 = log(k/0.01)==5033*((1/300)-(1/T));
Eq5 = K_c==10*exp(3020*((1/450)-(1/T)));
S = solve([Eq1,Eq2,Eq3,Eq4,Eq5])
K_c = S.K_c
T = S.T
k = S.k
r = S.r
x = S.x
producing:
K_c =
17.035850243008982963302938775977
T =
488.80156878875638115282331218132
k =
6.5200672012411590417154405645886
r =
-0.00037760313757751276230564662436265
x =
0.94400784394378190576411656090662
.
