Issue uploading files

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We're seeing the error when uploading a file in a C5.7.5.2 site:
[oode]Allowed memory size of 62914560 bytes exhausted (tried to allocate 13388113 bytes)[/code]

That suggests 62MB has been used up, the image is only 353KB.

The servers upload limit is set to 20MB and the PHP memory limit is set really high.

The host say:
"Looking at the Status page in PHP MyAdmin I can see some errors are occurring with the Handler_read_rnd functions. There are some suggestions shown as to how to resolve the issues with better indexing."

I don't know what that means really - how can we fix this?

Thanks
Dave

madesimplemedia