In[26]:= Solve[Gamma[x + 1] == (7!)!/7! && Abs[x - 5039] <= 10,
x] // N
During evaluation of In[26]:= Solve::nint: Warning: Solve used numeric integration to show that the solution set found is complete. >>
Out[26]= {{x -> 5039.}, {x -> 5039. - 0.737025 I}, {x ->
5039. + 0.737025 I}, {x -> 5039. - 1.47405 I}, {x ->
5039. + 1.47405 I}, {x -> 5039. - 2.21108 I}, {x ->
5039. + 2.21108 I}, {x -> 5039. - 2.9481 I}, {x ->
5039. + 2.9481 I}, {x -> 5039. - 3.68513 I}, {x ->
5039. + 3.68513 I}, {x -> 5039. - 4.42215 I}, {x ->
5039. + 4.42215 I}, {x -> 5039. - 5.15918 I}, {x ->
5039. + 5.15918 I}, {x -> 5039. - 5.8962 I}, {x ->
5039. + 5.8962 I}, {x -> 5039. - 6.63323 I}, {x ->
5039. + 6.63323 I}, {x -> 5039. - 7.37025 I}, {x ->
5039. + 7.37025 I}, {x -> 5039. - 8.10728 I}, {x ->
5039. + 8.10728 I}, {x -> 5039. - 8.8443 I}, {x ->
5039. + 8.8443 I}, {x -> 5039. - 9.58133 I}, {x ->
5039. + 9.58133 I}}