If you would prefer to keep the images as JPEGs, when you export (in5 > Export HTML5 with in5...), go to the Advanced section of the Export HTML5 with in5 dialog, and set Image Quality to Use Source Image (when available).
Here's more information on setting Image Quality:
I'm wondering if your image has been cropped by the frame that contains it. In that case, in5 will interpret the cropping to mean that you want it to generate a new image based on those cropping instructions. If you don't actually want to crop the image with the frame that contains it, select image and go to Object > Fitting > Fit Frame to Content.
All the jpeg images on the page are cropped by the Indesign frame. But only the one with a Hyperlink gets converted to PNG. An annoying a bug which is hopefully addressed in future updates.
I'm not able to reproduce your results. Using in5 version 3.8.7, I am able to place a JPEG, apply a hyperlink to it, export it with Image Quality set to Use Source Image (when available), and have the exported content use the original JPEG.
In order for our developers to address it, would you be able to send us your InDesign file or a sample file that recreates the issue and your html5_output folder? You can send it here: https://ajarproductions.com/pages/contact.php
You can go to https://ajarproductions.com/pages/contact.php?category=in5 and click on Report a problem or bug to get a field where you can send a link to your file.