No option for that yet. It would be easy to implement, but I'm not sure what the benefit would be - the searches only take up a tiny bit of memory, so is there some other disadvantage to having that many of them?
For years we had people asking for an option to clear the list of recent searches, and even though nobody would ever explain why, we eventually implemented it anyway (my sneaking suspicion is that people were looking up how to say things in Chinese that they were slightly embarrassed about), but now that that option's there I'm not sure what other benefit there might be to making the list shorter.