Most of my extensions are marked as compatible with 4.7 but do not explicitly say they will work with 5.0, 5.1, etc. Can I safely upgrade CiviCRM and continue to use the extensions?
Because 5.0 does not include breaking changes, it is considered equally compatible with 4.7 extensions. There is always minor risk of breakage when upgrading software, but 4.7 to 5.0 is not considered a major upgrade.
- In the 4.x series, tags mean the same as today. (Exact-match to version. An extension declaring 4.6 is not displayed for download on 4.7.)
- In the 5.x series, tags imply forward compatibility. (An extension declaring 5.2 is displayed on 5.2, 5.3, etc. But not on 5.0.)
- To bridge them, 4.7 is forward compatible with 5.0. (An extension declaring 4.7 is displayed on 4.7, 5.0, 5.1, etc.)
- As today, a consumer sees the newest extensions that are compatible with their version.
It is difficult to answer your question without detailed knowledge of your system and the extensions that you have installed.
The best way to find out if there are any issues is to take a copy of your site and upgrade this in a test environment. I would recommend that you do this in any case before applying any updates to your system.