Something similar to Mahler

Check out some of the Strauss tone poems - Don Juan, Til Eulenspiegel, Don Quixote ....

I think Bruckner is far from Mahler, nor Sibelius nor even Williams. I go more to R. Strauss and Shostikovich. Mayhap even Stravinski. It is so hard to associate near and kindred. He did not get the deserved exposure in his time. Bernstein did a lot for his legacy.
And come to think of it, you ask an odd sort of question, or at least unlikely. To me it is hard to have the sensibility to appreciate Mahler, but it is almost as if you somehow tripped over him by chance. I am really puzzled. Although I loved him at first listen, I wonder why you pick 3&5 (see, odd again ;-) rather than, say his 8th. Most interesting Rtn1.

I, too, find your question intriguing.
Perhaps the following:
Mahler 1 might be a very good complement to 3 and 5
Shostakovich 5 and 9
Sibelius 2
Ives 2
Dvorak 8 and 9
And:
Mahavishnu Orchestra - Inner Mounting Flame and Birds of Fire

Pick your favorite orchestras and conductors; they've all recorded much of the above, no doubt.

Closest match style wise would probably be Shostakovich, start with popular middle symphonies 5-10. Best to mix and match here but if you want one name I go with Jarvi/Chandos

Later Sibelius would also be sympathetic, the early 1,2 symphonies are romantic works similar to Tchaikovsky symphonies, Sibelius 3 is transitional and 4-6 would be close to Mahler 3,5.......the Maazel/London is an excellent Sibelius set.

Also along those line try Nielson 4,5,6 many good 2CD sets like Bloomstedt/London

Strauss tone poems......sure why not, unless you are seeking only symphonies

Bruckner is really a Wagner disciple, building layers of sound that ebb and flow like tidal waves, erecting massive "cathedrals of sound" Style wise really different than Mahler but Bruckner has works of great beauty that every classical fan must own......perhaps a common theme that filters through both composer's work is religious element.

Obvious comment but collect all Mahler symphonies if you don't already own.

Of course, Mahler 2nd symphony is the closest link to the 3rd. The 1st is a lightweight introduction compared to the 2nd. Mahler very much rooted in the central european - Austrian-Czech-Jewish tradition, so you really should look after composers coming from this tradition. Dvorak and smetana to a certain extent kin to Mahler in their recurring to folk songs in their large symphonic works. You should also hear some Hungarian composer. Karoly Goldmark is an interesting composer, his major opera, the Queen of Saba you can order from Hungaroton label. And of course, Bartok.