If the tuning increments are only 5 khz that would make receiving SSB impossible. The best way I know of to receive SSB very cheaply would be the direct sampling input on an RTLSDR blog version 3 RTL dongle, which should be able to receive HF using the unused Q input on the RTL chip. (its also good for locating RFI sources aroud the house, that actually is a big plus, my RTL dongle that I use for direct sampling is very good for locating RFI. Less so for HF, but still better than I expected.
What would be the best very cheap option would likely be an RTL dongle and an external up converter like the "Ham it up" or Adam's (9A4QV of LNA4all) design HF upconverter (very good) But be aware the limitations of an 8 bit SDR will be significant. You would still probably have a superior receive setup than youcould get otherwise for the price. If you have decent sound card you could likely build a better setup using a VFO, miser, etc. With a softrock type receiver the sound card will determine the sampling depth. Both upcoverters cost around $45 and maye 20 for the rtlsdr blog dongle and around $7-15 for other RTL dongles such as the newsky branded ones are quite consistant. They also source branded dongles to OEMS who want to put their brand on a USB dongle. so, for around $50 or $55 you can be listening to HF SSB and have a nice panalyzer/bandscope for ham radio that also can receive the VHF/UHF bands (but not as well as a ham rig, on any of them. Still for $20 surprisingly well. Atthe end of the day, you would never have expected to get what would have required a whole rack of equipment a couple of years ago to be in that little tiny package..