Is it appropriate to have two tables side by side in an academic thesis? I have about 5 relatively small tables which will be shown in the same part of my thesis. I think it might be a waste of space if I place one table per line, but I am not sure whether one should put e.g. 2 tables side by side in an academic thesis as I have never seen someone do this.

What is the convention?
The only rule here is to do what is best for your reader.  Try it different ways and see which presentation is simplest for the reader to interpret.  Some considerations to bear in mind are simple labelling of your tables and close proximity of the tables to any textual explanation of their contents.  Try to allow the reader to see the tables and accompanying textual explanations without having to flip back-and-forth between pages.  Your supervisor might be able to give you some guidance here, but the goal is to make the dissertation as clear and simple as possible.  The fact that you have not seen this before in a dissertation is not determinative of any problem with it.

If you find that you are presenting large amounts of information in tables, then another thing to bear in mind is that tables are usually a poor way to present large amounts of information, relative to appropriate graphs.  Consider whether you can present the same information graphically in a simple and clear manner, and relegate the accompanying tables to an appendix.  Again, you should be driven by consideration of what is best for your reader.  Always ask yourself: if I was reading this and had not seen it before, how would I want it presented to me?