no it should not. In rare cases the uvb can be too strong on some babies eyes but the Reptisun 5.0 should not cause a baby to close its eyes. There is something else going on there.
If the light is brand new, they can indeed cause babies to close their eyes. The lights have a burn in period where the UVB can be too intense for small/young/sensitive animals. I'm sorry, but I can't quite remember the exact burn in period, but I want to say it was something like a week. There is info on the forums about it that a search should bring up.